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# Applied category theory research progress

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51.
edited August 2018

29 September 2017:

This week's progress:

1) My paper with Nina Otter, Operads and phylogenetic trees, was finally accepted for publication by Theory and Applications of Categories! Steve Lack was the editor here. The referee had taken over a year to read our paper, and then given us a huge list of suggestions, so this is great news.

2) Blake Pollard's thesis is now on the arXiv:

Abstract. We define the concept of an 'open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of boundary states induce non-equilibrium steady states characterized by non-zero probability currents flowing through the system. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process.

We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of 'inputs' and 'outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. We construct a 'black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems.

3) Daniel Cicala submitted the final version of his paper Categorifying the zx-calculus to the conference proceedings Quantum Physics and Logic. This was already accepted for publication, so we can count this as yet another touchdown.

Comment Source:29 September 2017: This week's progress: 1) My paper with Nina Otter, <a href = "https://arxiv.org/abs/1512.03337">Operads and phylogenetic trees</a>, was finally accepted for publication by <i>Theory and Applications of Categories!</i> Steve Lack was the editor here. The referee had taken over a year to read our paper, and then given us a huge list of suggestions, so this is great news. 2) Blake Pollard's thesis is now on the arXiv: * <i><a href = "https://arxiv.org/abs/1709.09743">Open Markov Processes and Reaction Networks</a></i> > **Abstract.** We define the concept of an 'open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of boundary states induce non-equilibrium steady states characterized by non-zero probability currents flowing through the system. We show that these non-equilibrium steady states minimize a quadratic form which we call 'dissipation.' This is closely related to Prigogine's principle of minimum entropy production. We bound the rate of change of the entropy of a driven non-equilibrium steady state relative to the underlying equilibrium state in terms of the flow of probability through the boundary of the process. > We then consider open Markov processes as morphisms in a symmetric monoidal category by splitting up their boundary states into certain sets of 'inputs' and 'outputs.' Composition corresponds to gluing the outputs of one such open Markov process onto the inputs of another so that the probability flowing out of the first process is equal to the probability flowing into the second. We construct a 'black-box' functor characterizing the behavior of an open Markov process in terms of the space of possible steady state probabilities and probability currents along the boundary. The fact that this is a functor means that the behavior of a composite open Markov process can be computed by composing the behaviors of the open Markov processes from which it is composed. We prove a similar black-boxing theorem for reaction networks whose dynamics are given by the non-linear rate equation. Along the way we describe a more general category of open dynamical systems where composition corresponds to gluing together open dynamical systems. 3) Daniel Cicala submitted the final version of his paper <a href = "https://arxiv.org/abs/1704.07034">Categorifying the zx-calculus</a> to the conference proceedings Quantum Physics and Logic. This was already accepted for publication, so we can count this as yet another touchdown. 
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52.

October 5, 2017:

1) The really big news is that Blake has a postdoc job, using category theory to help design more stable electrical grids! He'll start around November 15th.

I think he'll be located at the National Institute of Science and Technology, in Maryland. But his position is funded through Carnegie Mellon University, thanks to an NSF: EAGER grant obtained by Eswaran Subrahmanian, a professor at The Institute for Complex Engineered Systems.

2) Right now Blake is doing an internship at Siemens, and he's giving some lectures on category theory:

At Arqui's request, I started giving daily 1-1.5 hour category theory lectures here at Siemens (just Arqui and the other intern I work with are in attendance). It has been pretty fun. This week, we more or less made it through your "Some definitions everyone should know." Next I'm going to explain lax monoidal functors and give them a quick introduction to the decorated cospan stuff. We typically break off into tangents trying to imagine how this stuff might be useful in engineering.

3) I can't resist mentioning that my paper with Nina on operads and phylogenetic trees has finally appeared. It may take a long for papers to be accepted by Theory and Application of Categories, but when they are, and you submit the paper in their preferred style, they're usually quite quick about publishing it!

Comment Source:October 5, 2017: 1) The really big news is that Blake has a postdoc job, using category theory to help design more stable electrical grids! He'll start around November 15th. I think he'll be located at the National Institute of Science and Technology, in Maryland. But his position is funded through Carnegie Mellon University, thanks to an <a href = "https://www.nsf.gov/about/transformative_research/submit.jsp">NSF: EAGER</a> grant obtained by <a href = "http://www.ices.cmu.edu/eswaran-subrahmanian.asp">Eswaran Subrahmanian</a>, a professor at <a href = "http://www.cmu.edu/ices/people/research-faculty.html">The Institute for Complex Engineered Systems</a>. 2) Right now Blake is doing an internship at Siemens, and he's giving some lectures on category theory: <blockquote>At Arqui's request, I started giving daily 1-1.5 hour category theory lectures here at Siemens (just Arqui and the other intern I work with are in attendance). It has been pretty fun. This week, we more or less made it through your "<a href = "http://math.ucr.edu/home/baez/qg-winter2001/definitions.pdf">Some definitions everyone should know</a>." Next I'm going to explain lax monoidal functors and give them a quick introduction to the decorated cospan stuff. We typically break off into tangents trying to imagine how this stuff might be useful in engineering.</blockquote> 3) I can't resist mentioning that my paper with Nina on operads and phylogenetic trees has <a href = "http://www.tac.mta.ca/tac/volumes/32/40/32-40.pdf">finally appeared</a>. It may take a long for papers to be accepted by Theory and Application of Categories, but when they are, and you submit the paper in their preferred style, they're usually quite quick about publishing it! 
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53.
edited August 2018

14 October 2018:

A lot of people are trying to finish up papers, but I don't know anything that was finished this week, so I just have an interesting story about (yet another) workshop on applied category theory.

Jelle Herold is a programmer who I've met at a couple of conferences; he likes Petri nets and category theory, but he's more of a hacker than a theorist. He sent out an email inviting a bunch of people to Croatia for a week early next month, to help his company use category theory to design new "blockchain" software. These people included David Spivak and me, and also Victor Winschel, whom Brendan knows, and who seems to be involved with Jelle's project.

David and I will be busy at my applied category theory special session, so I'm trying to get Christian Barrett Williams - a new math grad student at UCR, who is really interested in blockchain and category theory! - to take my place in Croatia. It seems to be working, but Christian needs to renew his passport first, so it's touch-and-go. I hope it works.

Here is Jelle's invitation:

Dear Sir,

On behalf of Statebox, you are cordially invited to attend our first official summit on category theory and blockchain technology, which will take place on the scenic island of Zlarin, Croatia between 1-7 November, 2017.

People involved in the Statebox project strongly believe that modern research in mathematics and computer science should have a paramount role in the design of software, in particular for the blockchain environment. Thus, the aim of this gathering is to bring together experts from different scientific fields and create a fertile ground for discussion and collaboration. By the end of this seven-day summit, we hope to have formed a strong community interested in what we do, willing to help us lay out the best mathematical formalization for its underlying core.

Comment Source:14 October 2018: A lot of people are trying to finish up papers, but I don't know anything that was <i>finished</i> this week, so I just have an interesting story about (yet another) workshop on applied category theory. Jelle Herold is a programmer who I've met at a couple of conferences; he likes Petri nets and category theory, but he's more of a hacker than a theorist. He sent out an email inviting a bunch of people to Croatia for a week early next month, to help his company use category theory to design new "blockchain" software. These people included David Spivak and me, and also Victor Winschel, whom Brendan knows, and who seems to be involved with Jelle's project. David and I will be busy at my applied category theory special session, so I'm trying to get Christian Barrett Williams - a new math grad student at UCR, who is really interested in blockchain and category theory! - to take my place in Croatia. It seems to be working, but Christian needs to renew his passport first, so it's touch-and-go. I hope it works. Here is Jelle's invitation: <blockquote> Dear Sir, <p> On behalf of Statebox, you are cordially invited to attend our first official summit on category theory and blockchain technology, which will take place on the scenic island of Zlarin, Croatia between 1-7 November, 2017. <p> People involved in the Statebox project strongly believe that modern research in mathematics and computer science should have a paramount role in the design of software, in particular for the blockchain environment. Thus, the aim of this gathering is to bring together experts from different scientific fields and create a fertile ground for discussion and collaboration. By the end of this seven-day summit, we hope to have formed a strong community interested in what we do, willing to help us lay out the best mathematical formalization for its underlying core. </blockquote> 
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54.
edited August 2018

23 October 2017:

Okay, now for this week's progress. The first item counts as next week's progress, but some of you may want to attend, to see what I do in my spare time:

1) I'm giving a talk next week:

• International Open Access Week, Wednesday 25 October 2017, 9:30–11:00 a.m., University of California, Riverside, Orbach Science Library, Room 240.
John Baez, Professor of Mathematics, UC Riverside: John will describe his activities to save US government climate data through his collaborative effort, the Azimuth Climate Data Backup Project. All of the saved data is now open access for everyone to utilize for research and scholarship.

My talk will be the first after the introduction. There will be refreshments, so hungry grad students should attend!

2) I fixed up my paper Quantum techniques for reaction networks, making some changes demanded by the referees.

This is another slow-burning story: I finished this paper in June 2013 shortly after finishing the companion paper Quantum techniques for studying equilibrium in chemical reaction networks with Brendan. The paper with Brendan got accepted pretty quickly by Journal of Complex Networks, and I submitted my own paper to same special issue of that journal, but some editor thought two papers in the same special issue was too much, so they shunted it off to a special issue of another journal, Natural Computing.

There it sat for several years, despite my queries! I finally heard back this September: it was accepted subject to some corrections. Now I've finally made those corrections. I shouldn't have waited so long.

Moral: never give up on a paper. And when it comes time to do more work on a paper, spring into action immediately.

There are a lot of other things going on, but nothing else that counts as "finished" except this:

3) Christian Williams went in to LA to renew his passport so he can attend the workshop on Petri nets and blockchains in Croatia during the first week of November. He's been invited to give a talk on open Petri nets!

Comment Source:23 October 2017: Okay, now for this week's progress. The first item counts as next week's progress, but some of you may want to attend, to see what I do in my spare time: 1) I'm giving a talk next week: <ul> <li> International Open Access Week, Wednesday 25 October 2017, 9:30–11:00 a.m., University of California, Riverside, Orbach Science Library, Room 240. </li> </ul> <blockquote> John Baez, Professor of Mathematics, UC Riverside: John will describe his activities to save US government climate data through his collaborative effort, the Azimuth Climate Data Backup Project. All of the saved data is now open access for everyone to utilize for research and scholarship. </blockquote> My talk will be the first after the introduction. There will be refreshments, so hungry grad students should attend! 2) I fixed up my paper <a href = "https://arxiv.org/abs/1306.3451">Quantum techniques for reaction networks</a>, making some changes demanded by the referees. This is another slow-burning story: I finished this paper in June 2013 shortly after finishing the companion paper <a href = "http://arxiv.org/abs/1305.4988">Quantum techniques for studying equilibrium in chemical reaction networks</a> with Brendan. The paper with Brendan got accepted pretty quickly by <i>Journal of Complex Networks</i>, and I submitted my own paper to same special issue of that journal, but some editor thought two papers in the same special issue was too much, so they shunted it off to a special issue of another journal, <i>Natural Computing</i>. There it sat for several years, despite my queries! I finally heard back this September: it was accepted subject to some corrections. Now I've finally made those corrections. I shouldn't have waited so long. Moral: never give up on a paper. And when it comes time to do more work on a paper, spring into action immediately. There are a lot of other things going on, but nothing else that counts as "finished" except this: 3) Christian Williams went in to LA to renew his passport so he can attend the workshop on Petri nets and blockchains in Croatia during the first week of November. He's been invited to give a talk on open Petri nets! 
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55.

29 October 2017:

This week's progress:

1) I finally submitted my grant proposal to the NSF - it took a long time to fight its way through the UCR bureaucracy. If accepted, it could pay for 4 grad students from UCR to attend the applied category theory school in Leiden, Monday April 23rd to Thursday April 26th. So don't forget:

The deadline for applying to the school is this Wednesday, November 1st. To apply, go here.

So far I have some evidence that Joseph, Daniel and Kenny have applied... and I think Jade said he would too.

2) Jason wrote a great article about graphical linear algebra on Pawel Sobocinski's blog:

Lots of marvelous string diagrams! He and Pawel have been chopping down the number of relations needed to present the prop of finite-dimensional vector space and linear relations.

ALSO:

People giving talks at the special session next weekend are welcome to practice their talks this Wednesday in the collaboration room. One of you should get the projector from James Marberry.

John Foley from Metron will be showing up Wednesday in the early afternoon, so he'll get a sneak preview of some talks... but also, let's have some fun math conversations! He will be around Thursday and Friday and probably eager to talk to folks, especially Joseph (since he's working on the same project with John and me), but also everyone else.

A bunch of us will go out to dinner on Saturday and Sunday, including David Spivak and his gang. So, get ready for fun!

But before that, some of us have gotta finish some papers...

Comment Source:29 October 2017: This week's progress: 1) I finally submitted my grant proposal to the NSF - it took a long time to fight its way through the UCR bureaucracy. If accepted, it could pay for 4 grad students from UCR to attend the applied category theory school in Leiden, Monday April 23rd to Thursday April 26th. So don't forget: The deadline for applying to the school is this Wednesday, November 1st. To apply, go here. So far I have some evidence that Joseph, Daniel and Kenny have applied... and I think Jade said he would too. 2) Jason wrote a great article about graphical linear algebra on Pawel Sobocinski's blog: * <a href = "https://graphicallinearalgebra.net/2017/10/23/episode-r1-redundancy-and-zebra-snakes/">Episode R1: Redundancy and Zebra Snakes</a>. Lots of marvelous string diagrams! He and Pawel have been chopping down the number of relations needed to present the prop of finite-dimensional vector space and linear relations. ALSO: People giving talks at the special session next weekend are welcome to practice their talks this Wednesday in the collaboration room. One of you should get the projector from James Marberry. John Foley from Metron will be showing up Wednesday in the early afternoon, so he'll get a sneak preview of some talks... but also, let's have some fun math conversations! He will be around Thursday and Friday and probably eager to talk to folks, especially Joseph (since he's working on the same project with John and me), but also everyone else. A bunch of us will go out to dinner on Saturday and Sunday, including David Spivak and his gang. So, get ready for fun! But before that, some of us have gotta finish some papers...
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56.

4 November 2017:

We made a lot of progress this week, completing 3 big papers. I apologize for becoming pretty bad-tempered during this time... I was pretty stressed. But now I'm happy, because we have a lot to show the folks coming to our special AMS session tomorrow!

1) Adam has been working on Hamiltonian and Lagrangian mechanics from an "open systems" point of view, and this week he put this paper on ths arXiv:

Abstract. Using the framework of category theory, we formalize the heuristic principles that physicists employ in constructing the Hamiltonians for open classical systems as sums of Hamiltonians of subsystems. First we construct a category where the objects are symplectic manifolds and the morphisms are spans whose legs are surjective Poisson maps. Using a slight variant of Fong's theory of "decorated" cospans, we then decorate the apices of our spans with Hamiltonians. This gives a category where morphisms are open classical systems, and composition allows us to build these systems from smaller pieces.

He also gets a functor from a category of Lagrangian open systems to this category of Hamiltonian systems.

2) Kenny and I have been continuing Blake and Brendan's work on open Markov processes, bringing 2-morphisms into the game. We put this on the arXiv:

Abstract. Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states. Here we extend coarse-graining to open Markov processes. An "open" Markov process is one where probability can flow in or out of certain states called "inputs" and "outputs". One can build up an ordinary Markov process from smaller open pieces in two basic ways: composition, where we identify the outputs of one open Markov process with the inputs of another, and tensoring, where we set two open Markov processes side by side. In previous work, Fong, Pollard and the first author showed that these constructions make open Markov processes into the morphisms of a symmetric monoidal category. Here we go further by constructing a symmetric monoidal double category where the 2-morphisms are ways of coarse-graining open Markov processes. We also extend the already known "black-boxing" functor from the category of open Markov processes to our double category. Black-boxing sends any open Markov process to the linear relation between input and output data that holds in steady states, including nonequilibrium steady states where there is a nonzero flow of probability through the process. To extend black-boxing to a functor between double categories, we need to prove that black-boxing is compatible with coarse-graining.

3) Our project with DARPA has finally given birth to a paper! I hope this is just the first; it starts laying down the theoretical groundwork for designing networked systems. John is here now and we're coming up with a bunch of new ideas:

• John Baez, John Foley, Joseph Moeller and Blake Pollard, Network models.
Abstract. Networks can be combined in many ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of networks. We show that each network model gives rise to an operad, whose operations are ways of assembling a network of the given kind from smaller parts. Such operads, and their algebras, can serve as tools for designing networks. Technically, a network model is a lax symmetric monoidal functor from the free symmetric monoidal category on some set to Cat, and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction.

See you at our special session at 9 am in Room 268 of the HUB on Saturday! Registration starts around 7:30 on the 3rd floor of the same building! Anyone who wants to should join us for dinner Saturday and Sunday night.

Comment Source:4 November 2017: We made a lot of progress this week, completing 3 big papers. I apologize for becoming pretty bad-tempered during this time... I was pretty stressed. But now I'm happy, because we have a lot to show the folks coming to our special AMS session tomorrow! 1) Adam has been working on Hamiltonian and Lagrangian mechanics from an "open systems" point of view, and this week he put this paper on ths arXiv: <ul> <li>Adam Yassine, <a href = "https://arxiv.org/abs/1710.11392">Open systems in classical mechanics</a>. </li> </ul> <blockquote><b>Abstract.</b> Using the framework of category theory, we formalize the heuristic principles that physicists employ in constructing the Hamiltonians for open classical systems as sums of Hamiltonians of subsystems. First we construct a category where the objects are symplectic manifolds and the morphisms are spans whose legs are surjective Poisson maps. Using a slight variant of Fong's theory of "decorated" cospans, we then decorate the apices of our spans with Hamiltonians. This gives a category where morphisms are open classical systems, and composition allows us to build these systems from smaller pieces. </blockquote> He also gets a functor from a category of Lagrangian open systems to this category of Hamiltonian systems. 2) Kenny and I have been continuing Blake and Brendan's work on open Markov processes, bringing 2-morphisms into the game. We put this on the arXiv: <ul> <li>John Baez and Kenny Courser, <a href = "https://arxiv.org/abs/1710.11343">Coarse-graining open Markov processes</a>. </li> </ul> <blockquote><b>Abstract</b>. Coarse-graining is a standard method of extracting a simple Markov process from a more complicated one by identifying states. Here we extend coarse-graining to open Markov processes. An "open" Markov process is one where probability can flow in or out of certain states called "inputs" and "outputs". One can build up an ordinary Markov process from smaller open pieces in two basic ways: composition, where we identify the outputs of one open Markov process with the inputs of another, and tensoring, where we set two open Markov processes side by side. In previous work, Fong, Pollard and the first author showed that these constructions make open Markov processes into the morphisms of a symmetric monoidal category. Here we go further by constructing a symmetric monoidal double category where the 2-morphisms are ways of coarse-graining open Markov processes. We also extend the already known "black-boxing" functor from the category of open Markov processes to our double category. Black-boxing sends any open Markov process to the linear relation between input and output data that holds in steady states, including nonequilibrium steady states where there is a nonzero flow of probability through the process. To extend black-boxing to a functor between double categories, we need to prove that black-boxing is compatible with coarse-graining.</blockquote> 3) Our project with DARPA has finally given birth to a paper! I hope this is just the first; it starts laying down the theoretical groundwork for designing networked systems. John is here now and we're coming up with a bunch of new ideas: <ul> <li> John Baez, John Foley, Joseph Moeller and Blake Pollard, <a href = "https://arxiv.org/abs/1711.00037">Network models</a>. </li> </ul> <blockquote><b>Abstract.</b> Networks can be combined in many ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of networks. We show that each network model gives rise to an operad, whose operations are ways of assembling a network of the given kind from smaller parts. Such operads, and their algebras, can serve as tools for designing networks. Technically, a network model is a lax symmetric monoidal functor from the free symmetric monoidal category on some set to Cat, and the construction of the corresponding operad proceeds via a symmetric monoidal version of the Grothendieck construction. </blockquote> I blogged about this last one here: <ul> <li> <a href = "https://johncarlosbaez.wordpress.com/2017/10/31/complex-adaptive-systems-part-6/">Complex adaptive systems (part 6).</a> </li> </ul> See you at our special session at 9 am in Room 268 of the HUB on Saturday! Registration starts around 7:30 on the 3rd floor of the same building! Anyone who wants to should join us for dinner Saturday and Sunday night. 
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57.

12 November 2017:

A huge amount of progress this week!

1) Most of the people on this list gave talks at the AMS special session on applied category theory. Almost all the talk slides from this session are here now:

We had lots of great conversations with all the visitors, and I have piles of new ideas to work on.

2) Christian Barrett Williams went to the Statebox conference in Croatia, and came back and gave a report on Wednesday.

3) Joseph Moeller went to visit Metron and attend a meeting where they showed off their work to DARPA. I hope he'll give us a report next Wednesday.

Comment Source:12 November 2017: A huge amount of progress this week! 1) Most of the people on this list gave talks at the AMS special session on applied category theory. Almost all the talk slides from this session are here now: <ul> <li> <a href = "http://math.ucr.edu/home/baez/ACT2017/">Applied Category Theory 2017</a>. </li> </ul> We had lots of great conversations with all the visitors, and I have piles of new ideas to work on. 2) Christian Barrett Williams went to the <a href = "http://statebox.org/zlarin-2017-info.html">Statebox conference</a> in Croatia, and came back and gave a report on Wednesday. 3) Joseph Moeller went to visit Metron and attend a meeting where they showed off their work to DARPA. I hope he'll give us a report next Wednesday.
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58.
edited September 2018

21 November 2017:

This week's - or really last week's - progress:

1) Daniel got this paper accepted by TAC, subject to very minor revisions. It's a great paper and you should all read it - I tend to assume you all read each other's papers to keep up with what's happening, but I fear that's not true. By now I realize this paper is just the beginning of using topos theory to study networks:

Abstract. We introduce the notion of a span of cospans and define, for them, horizonal and vertical composition. When in a topos C, these compositions satisfy the interchange law. A bicategory is then constructed from C-objects, C-cospans, and doubly monic spans of C-cospans. The primary motivation for this construction is an application to graph rewriting.

By the way, Daniel, you should fix the typo in the first sentence of the abstract! Also I think "these compositions satisfy the interchange law" is false unless the spans have monic legs. When you make all the fixes please put a new version on the abstract, and please send me a copy.

2) I gave the weekly General Biology Seminar at Caltech, and gave this talk:

Abstract. If biology is the study of self-replicating entities, and we want to understand the role of information, it makes sense to see how information theory is connected to the 'replicator equation' — a simple model of population dynamics for self-replicating entities. The relevant concept of information turns out to be the information of one probability distribution relative to another, also known as the Kullback–Leibler divergence. Using this we can get a new outlook on free energy, see evolution as a learning process, and give a clearer, more general formulation of Fisher's fundamental theorem of natural selection.

It was a bit scary talking to a large room of biologists about biology, but it went well. I spent the day talking to lots of people, mainly associated to Eric Winfree's gang — he studies the computational power of chemical reaction networks. For example, he found a chemical reaction network with two species such that in equilibrium the probability that it has any number of the two species, plotted in gray-scale, looks like a cartoon of Darth Vader. (He can get any probability distribution he wants.)

There are a lot of people at Caltech working on artificial neural networks and also on control theory in biology. I should get to know some of them!

Comment Source:21 November 2017: This week's - or really last week's - progress: 1) Daniel got this paper accepted by <i>TAC</i>, subject to very minor revisions. It's a great paper and you should all read it - I tend to assume you all read each other's papers to keep up with what's happening, but I fear that's not true. By now I realize this paper is just the beginning of using topos theory to study networks: <ul> <li>Daniel Cicala, <a href = "https://arxiv.org/abs/1611.07886">Spans of cospans</a>. </li> </ul> <blockquote><b>Abstract.</b> We introduce the notion of a span of cospans and define, for them, horizonal and vertical composition. When in a topos C, these compositions satisfy the interchange law. A bicategory is then constructed from C-objects, C-cospans, and doubly monic spans of C-cospans. The primary motivation for this construction is an application to graph rewriting. </blockquote> By the way, Daniel, you should fix the typo in the first sentence of the abstract! Also I think "these compositions satisfy the interchange law" is false unless the spans have monic legs. When you make all the fixes please put a new version on the abstract, and please send me a copy. 2) I gave the weekly General Biology Seminar at Caltech, and gave this talk: <ul> <li> <a href = "http://math.ucr.edu/home/baez/bio_asu/">Biology as information dynamics</a>. </li> </ul> <blockquote> <b> Abstract. </b> If biology is the study of self-replicating entities, and we want to understand the role of information, it makes sense to see how information theory is connected to the 'replicator equation' — a simple model of population dynamics for self-replicating entities. The relevant concept of information turns out to be the information of one probability distribution relative to another, also known as the Kullback&ndash;Leibler divergence. Using this we can get a new outlook on free energy, see evolution as a learning process, and give a clearer, more general formulation of Fisher's fundamental theorem of natural selection. </blockquote> It was a bit scary talking to a large room of biologists about biology, but it went well. I spent the day talking to lots of people, mainly associated to Eric Winfree's gang &mdash; he studies the computational power of chemical reaction networks. For example, he found a chemical reaction network with two species such that in equilibrium the probability that it has any number of the two species, plotted in gray-scale, looks like a cartoon of Darth Vader. (He can get any probability distribution he wants.) There are a lot of people at Caltech working on artificial neural networks and also on control theory in biology. I should get to know some of them!
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59.
edited September 2018

@John this topic is very cool !! I interpret it as a great opportunity to learn a bit about your way to conduct scientific activity.. , at #56 / 3) the "lax " of "symmetric monoidal" is simply not related to the ["Lax" (a name ) pairs], isn't it?

Comment Source:@John this topic is very cool !! I interpret it as a great opportunity to learn a bit about your way to conduct scientific activity.. , at #56 / 3) the "lax " of "symmetric monoidal" is simply not related to the ["Lax" (a name ) pairs], isn't it?
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60.

Indeed. Its "lax" as antonym to "strict": "The middle school has a lax dress code, but the high school's is really strict."

Comment Source:Indeed. Its "lax" as antonym to "strict": "The middle school has a lax dress code, but the high school's is really strict."
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61.

Thanks @Christopher

Comment Source:Thanks @Christopher
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62.
edited September 2018

27 November 2017:

This week's progress:

1) A total of 77 students applied for the "adjoint school" of Applied Category Theory 2017. 16 were chosen, and I believe they include these lucky folks:

• Daniel Cicala (part of the group working with Pawel Sobocinski on "Modelling of open and interconnected systems")
• Jade Master (part of the group working with Martha Lewis on "Compositional approaches to linguistics and cognition")
• Joseph Moeller (part of the group working with Aleks Kissinger on "Unification of the logic of causality")

2) After 841 days, the referee finally coughed up a report on a paper that Brendan Fong and I had submitted to TAC, A compositional framework for passive linear networks. The report is very detailed, about 8 pages long, and says our paper should be published "in some form" but demands major revisions, mainly shortening the paper. While this is tiresome, I think we can do it, since the referee explains exactly how - and I think our paper will be improved.

This quote says it all:

This paper has a wonderfully interesting subject matter, and with well-chosen notations and terminology, and a better-structured, more concise presentation, it could be a "gem". But in its current state, I found that even though I was motivated to read the paper, and even though I think I am a pretty close approximation of the intended audience, it took me many months and lots of stamina to fight my way through it.

It's worth a bit of extra work to create a "gem".

3) Last Monday I attended Paul-André Melliès' habilitation defense, along with

• the category theorist / computer scientist Gordon Plotkin
• the co-inventor of braided monoidal categories and the inventor of combinatorial species, André Joyal,
• the inventor of linear logic, Jean-Yves Girard,
• the computer scientist Thierry Coquand who gave his name to the programming language Coq,
• the mathematician Pierre-Louis Curien, an expert on rewriting theory
• the mathematician George Gonthier who came up with a fully formalized proof of the 4-color theorem using Coq, and
• Karine Chemla, an expert on the history of Chinese mathematics who is a friend of Lisa's - I was surprised to see her there!

Paul-André passed his defense, and I spent the rest of the week talking to him about the connection between star-autonomous categories, compact closed categories, Frobenius monoids, topological quantum field theory and logic.

There's a big mystery here: there seems to be some primitive form of logic which has topological quantum field theory and propositional logic as special cases, and we'd like to know why. He wants to invite me to Paris for 3 months sometime to work on this. That would be great.

On Tuesday I gave a talk on "our stuff"

• Compositionality in network theory
Abstract. To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. In principle all these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. This has been known for some time. However, the details are more challenging, and ultimately more rewarding, than this basic insight. Two complementary approaches are presentations of symmetric monoidal categories using generators and relations (which are more algebraic in flavor) and decorated cospan categories (which are more geometrical). In this talk we focus on the latter.

André Joyal liked it a lot and said he wanted to read some of our papers. Nicholas Behr had some very interesting ideas on chemistry as a stochastic process of graph rewriting (since molecules are like graphs), and pointed me to these papers he helped write:

I think we should work on this stuff, since we've got all the techniques! I also had a great conversation with Mathieu Anel on how symplectic geometry shows up in both classical mechanics and thermodynamics, which revived my dream of somehow unifying quantum mechanics and statistical mechanics. He gave me some clues that might overcome the obstacles I'd been stuck on.

So, a great visit!

Comment Source:27 November 2017: This week's progress: 1) A total of 77 students applied for the "adjoint school" of Applied Category Theory 2017. 16 were chosen, and I believe they include these lucky folks: <ul> <li> Daniel Cicala (part of the group working with Pawel Sobocinski on "Modelling of open and interconnected systems") </li> <li> Jade Master (part of the group working with Martha Lewis on "Compositional approaches to linguistics and cognition") </li> <li> Joseph Moeller (part of the group working with Aleks Kissinger on "Unification of the logic of causality") </li> </ul> 2) After 841 days, the referee finally coughed up a report on a paper that Brendan Fong and I had submitted to <i>TAC</i>, <a href = "https://arxiv.org/abs/1504.05625">A compositional framework for passive linear networks</a>. The report is very detailed, about 8 pages long, and says our paper should be published "in some form" but demands major revisions, mainly shortening the paper. While this is tiresome, I think we can do it, since the referee explains exactly how - and I think our paper will be improved. This quote says it all: <blockquote> This paper has a wonderfully interesting subject matter, and with well-chosen notations and terminology, and a better-structured, more concise presentation, it could be a "gem". But in its current state, I found that even though I was motivated to read the paper, and even though I think I am a pretty close approximation of the intended audience, it took me many months and lots of stamina to fight my way through it. </blockquote> It's worth a bit of extra work to create a "gem". 3) Last Monday I attended Paul-Andr&eacute; Melli&egrave;s' habilitation defense, along with <ul> <li> the category theorist / computer scientist Gordon Plotkin </li> <li> the co-inventor of braided monoidal categories and the inventor of combinatorial species, Andr&eacute; Joyal, </li> <li> the inventor of linear logic, Jean-Yves Girard, </li> <li> the computer scientist Thierry Coquand who gave his name to the programming language Coq, </li> <li> the mathematician Pierre-Louis Curien, an expert on rewriting theory </li> <li> the mathematician George Gonthier who came up with a fully formalized proof of the 4-color theorem using Coq, and </li> <li> Karine Chemla, an expert on the history of Chinese mathematics who is a friend of Lisa's - I was surprised to see her there! </li> </ul> Paul-Andr&eacute; passed his defense, and I spent the rest of the week talking to him about the connection between star-autonomous categories, compact closed categories, Frobenius monoids, topological quantum field theory and logic. There's a big mystery here: there seems to be some primitive form of logic which has topological quantum field theory and propositional logic as special cases, and we'd like to know why. He wants to invite me to Paris for 3 months sometime to work on this. That would be great. On Tuesday I gave a talk on "our stuff" <ul> <li> Compositionality in network theory </li> </ul> <blockquote> <b>Abstract.</b> To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. In principle all these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. This has been known for some time. However, the details are more challenging, and ultimately more rewarding, than this basic insight. Two complementary approaches are presentations of symmetric monoidal categories using generators and relations (which are more algebraic in flavor) and decorated cospan categories (which are more geometrical). In this talk we focus on the latter. </blockquote> Andr&eacute; Joyal liked it a lot and said he wanted to read some of our papers. Nicholas Behr had some very interesting ideas on chemistry as a stochastic process of graph rewriting (since molecules are like graphs), and pointed me to these papers he helped write: <ul> <li> Nicolas Behr, Vincent Danos, Ilias Garnier and Tobias Heindel, <a href = "https://arxiv.org/abs/1612.06240">The algebras of graph rewriting</a>. </li> <li> Nicolas Behr, Vincent Danos and Ilias Garnier, <a href = "https://hal.archives-ouvertes.fr/hal-01429645/document">Stochastic mechanics of graph rewriting</a>. </li> </ul> I think we should work on this stuff, since we've got all the techniques! I also had a great conversation with Mathieu Anel on how symplectic geometry shows up in both classical mechanics and thermodynamics, which revived my dream of somehow unifying quantum mechanics and statistical mechanics. He gave me some clues that might overcome the obstacles I'd been stuck on. So, a great visit! 
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63.

1 December 2017:

This week's progress, as far as I can remember:

1) Brandon Coya is going to have a skype interview for a tenure-track job at Providence College in Rhode Island! The interview is on December 11th.

He's a bit worried about being able to respond to the questions they throw at him. So, whenever you walk by him, ask him a tough job interview question!

Comment Source:1 December 2017: This week's progress, as far as I can remember: 1) Brandon Coya is going to have a skype interview for a tenure-track job at <a href = "http://www.providence.edu/">Providence College</a> in Rhode Island! The interview is on December 11th. He's a bit worried about being able to respond to the questions they throw at him. So, whenever you walk by him, ask him a tough job interview question! 
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64.
edited September 2018

9 December 2017:

Here is this week's progress:

1) Brandon will be doing another job interview, this time for a 2-year "teaching postdoc" at the University of Minnesota. Go, Brandon, go!

2) Daniel and Kenny got a referee's report on their paper Spans of cospans in a topos. The referee rejected the paper, which doesn't sound like progress... but the referee did so on the basis of counterexample that completely ignored one of the conditions in their theorem! So they wrote to the editor at TAC in charge of their paper, and I'm hoping they'll have better luck now.

3) I finished a paper I was invited to write for the forthcoming new and improved Newsletter of the London Mathematical Society: From the icosahedron to E8. It's about two ways to get E8 from the icosahedron - fun stuff, full of beautiful pictures.

4) I was invited to give a plenary talk at the "International conference on operad theory and related topics'' at Anhui University, in Hefei, China from November 5-9, 2018. I probably won't go, because it's a long flight followed by a long train ride for a short conference.

5) John Foley pointed out another applied category theory job - see the amazing words in boldface:

Multiple post-doctoral positions are open at the University of Maryland, College Park, to study fundamental mathematical and computational techniques for the conceptual design of engineered systems. Specifically, we are looking for talented researchers with expertise and a publication track-record in one (or more) of the following areas:
• Design Theory and Methodology, for example, in Computational Design Synthesis for engineering systems involving the interplay of function, behavior, and structure.
• Data-Driven Design and Optimization, for example, simulation-based design, multi-fidelity optimization, robotics, or optimal control.
• Computer Science, for example, machine learning/AI, software architecture, functional programming, lambda-calculus, and computer graphics/geometry.
• Applied Mathematics, for example, operator algebras, category theory, differential geometry, topology, or mathematical logic.
The appointments will be in the Department of Mechanical Engineering, full-time, for at least one-year with the possibility of renewals pending satisfactory performance and funding. Remuneration will be competitive and based on qualifications. The expected start date is January, 2018, though earlier or later state dates are negotiable. Applicants will be considered on a continuing basis until the positions are filled.
Comment Source:9 December 2017: Here is this week's progress: 1) Brandon will be doing another job interview, this time for a 2-year "teaching postdoc" at the University of Minnesota. Go, Brandon, go! 2) Daniel and Kenny got a referee's report on their paper <a href = "https://arxiv.org/abs/1707.02098">Spans of cospans in a topos</a>. The referee rejected the paper, which doesn't sound like progress... but the referee did so on the basis of counterexample that completely ignored one of the conditions in their theorem! So they wrote to the editor at <i>TAC</i> in charge of their paper, and I'm hoping they'll have better luck now. 3) I finished a paper I was invited to write for the forthcoming new and improved Newsletter of the London Mathematical Society: <a href = "https://arxiv.org/abs/1712.06436">From the icosahedron to E8</a>. It's about two ways to get E8 from the icosahedron - fun stuff, full of beautiful pictures. 4) I was invited to give a plenary talk at the "International conference on operad theory and related topics'' at Anhui University, in Hefei, China from November 5-9, 2018. I probably won't go, because it's a long flight followed by a long train ride for a short conference. 5) John Foley pointed out another applied category theory job - see the amazing words in boldface: <blockquote> Multiple post-doctoral positions are open at the University of Maryland, College Park, to study fundamental mathematical and computational techniques for the conceptual design of engineered systems. Specifically, we are looking for talented researchers with expertise and a publication track-record in one (or more) of the following areas: <ul> <li>Design Theory and Methodology, for example, in Computational Design Synthesis for engineering systems involving the interplay of function, behavior, and structure. </li> <li> Data-Driven Design and Optimization, for example, simulation-based design, multi-fidelity optimization, robotics, or optimal control. </li> <li>Computer Science, for example, machine learning/AI, software architecture, functional programming, lambda-calculus, and computer graphics/geometry. </li> <li>Applied Mathematics, for example, operator algebras, <b>category theory</b>, differential geometry, topology, or mathematical logic. </li> </ul> The appointments will be in the Department of Mechanical Engineering, full-time, for at least one-year with the possibility of renewals pending satisfactory performance and funding. Remuneration will be competitive and based on qualifications. The expected start date is January, 2018, though earlier or later state dates are negotiable. Applicants will be considered on a continuing basis until the positions are filled. </blockquote> 
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65.

20 December 2017:

Here is this week's progress, as far as I know:

1) I told you last time how Kenny and Daniel's paper was rejected from TAC based on a mistaken counterexample to their main theorem. They explained this to the editor and referee, and now their paper has been accepted!

The new referee's report is so nice I'm going to quote it:

This is a nice, carefully written paper which presents a new and interesting result. I recommend that it be accepted for TAC. The authors continue the study of the bicategory of cospans in a topos introduced by the first author in "Spans of cospans" to appear in TAC. Their motivation lies in the theory of complex networks and in order to accommodate the various constructions that they wish to perform, they must take as 2-cells, not the usual morphisms of cospans, but monic spans of cospans. Their main result is that this gives a symmetric compact closed bicategory. Now, this bicategory is relatively complicated, and proving that any bicategory is symmetric monoidal, let alone compact, is no mean feat. To accomplish this, the authors use a theorem of Shulman's which constructs a symmetric monoidal bicategory from an isobrant symmetric monoidal double category. This last structure sounds more complicated but in fact it is much easier to use because the coherences are isomorphisms rather than equivalences. So they enlarge their bicategory to a double category in which the vertical arrows are isomorphisms rather than the identities which are the hallmark of a bicategory. This seemingly minor change allows the coproduct to be a monoidal structure on the objects and then Shulman's theorem applies. Once this double category has done its job it is summarily discarded. Shulman's theorem cannot be used to get compactness, so the authors resort to a theorem of Pstragowski for this.

Lately I've been feeling we should not "summarily discard" the double categories that Kenny has been using to build bicategories - that's a nice observation by the referee, with a nice touch of humor.

There probably is a Shulman-esque theorem that says "given a .... double category you get a compact closed symmetric monoidal bicategory", and I bet Kenny and Daniel could easily extract this theorem from the argument they used in this special case. Maybe Kenny should do that in his thesis!

2) Now I have a paper that seems to have been erroneously rejected despite a very positive referee's report.

This is not really progress; I'm mentioning it just because it outraged me. Here is the letter I received:

Dear Prof. Baez,

We have received the reports from our advisors on your manuscript NACO-D-14-00036R1 "Quantum Techniques for Reaction Networks".

With regret, I must inform you that, based on the advice received, the Editors have decided that your manuscript cannot be accepted for publication in Natural Computing.

I would like to thank you very much for forwarding your manuscript to us for consideration and wish you every success in finding an alternative place of publication.

With kind regards, Journals Editorial Office Springer

Reviewer #4: The manuscript entitled "Quantum Techniques for Reaction Networks" investigates reaction networks utilizing quantum mechanical tools. Given a set of species and transitions which takes complexes to each other, the author derived the equations that governs concentration of the species. From a continuous-deterministic point of view, he derived rate equation for expected number of population of each species and from a discrete-stochastic point of view (by leveraging the probabilistic interpretation of amplitudes in quantum theory and using operators), he was able to obtain the underlying master equation. Then he made a connection between the state vector of the rate equation (classical state) and state vector of the master equation (mixed state) by averaging over probability distribution of the second one(amplitudes). Finally the author shows the required condition where both equations and formalism can be equivalent, which is large number limit and coherent regime.

I am completely satisfied with this paper. Its a coherent and well-written paper with a new approach to reaction networks. This view may be of interest not only for researchers in this field but also for people in entire network society. I strongly recommend this paper for publication in this journal. Besides, I have two questions for the author and I suggest him to rephrase these questions and add them as future works in the last part of the paper (Its up to the author to do this or not).

1-Relation between rate equation and master equation has been discussed in the regime of the mass-action law. Does it work in other regimes?

2-The author has derived the exact relation between rate equation formalism and master equation formalism when the initial state is a coherent state. Is it possible to have a non-coherent state which satisfy the equivalence condition (stated under the theorem 8)?

Aargh! Emphasis mine: I've never gotten such a positive referee's report together with a rejection. I've asked some flunky at Springer to look into it, and I'll see what they have to say.

Comment Source:20 December 2017: Here is this week's progress, as far as I know: 1) I told you last time how Kenny and Daniel's paper was rejected from <i>TAC</i> based on a mistaken counterexample to their main theorem. They explained this to the editor and referee, and now their paper has been accepted! The new referee's report is so nice I'm going to quote it: <blockquote> This is a nice, carefully written paper which presents a new and interesting result. I recommend that it be accepted for TAC. The authors continue the study of the bicategory of cospans in a topos introduced by the fi rst author in "Spans of cospans" to appear in TAC. Their motivation lies in the theory of complex networks and in order to accommodate the various constructions that they wish to perform, they must take as 2-cells, not the usual morphisms of cospans, but monic spans of cospans. Their main result is that this gives a symmetric compact closed bicategory. Now, this bicategory is relatively complicated, and proving that any bicategory is symmetric monoidal, let alone compact, is no mean feat. To accomplish this, the authors use a theorem of Shulman's which constructs a symmetric monoidal bicategory from an iso brant symmetric monoidal double category. This last structure sounds more complicated but in fact it is much easier to use because the coherences are isomorphisms rather than equivalences. So they enlarge their bicategory to a double category in which the vertical arrows are isomorphisms rather than the identities which are the hallmark of a bicategory. This seemingly minor change allows the coproduct to be a monoidal structure on the objects and then Shulman's theorem applies. Once this double category has done its job it is summarily discarded. Shulman's theorem cannot be used to get compactness, so the authors resort to a theorem of Pstragowski for this. </blockquote> Lately I've been feeling we should not "summarily discard" the double categories that Kenny has been using to build bicategories - that's a nice observation by the referee, with a nice touch of humor. There probably is a Shulman-esque theorem that says "given a .... double category you get a compact closed symmetric monoidal bicategory", and I bet Kenny and Daniel could easily extract this theorem from the argument they used in this special case. Maybe Kenny should do that in his thesis! 2) Now I have a paper that seems to have been erroneously rejected despite a very positive referee's report. This is not really progress; I'm mentioning it just because it outraged me. Here is the letter I received: <blockquote> Dear Prof. Baez, <p> We have received the reports from our advisors on your manuscript NACO-D-14-00036R1 "Quantum Techniques for Reaction Networks". <p> With regret, I must inform you that, based on the advice received, the Editors have decided that your manuscript cannot be accepted for publication in Natural Computing. <p> Below, please find the comments for your perusal. <p> I would like to thank you very much for forwarding your manuscript to us for consideration and wish you every success in finding an alternative place of publication. <p> With kind regards, Journals Editorial Office Springer </blockquote> <blockquote> COMMENTS TO THE AUTHOR: <p> Reviewer #4: The manuscript entitled "Quantum Techniques for Reaction Networks" investigates reaction networks utilizing quantum mechanical tools. Given a set of species and transitions which takes complexes to each other, the author derived the equations that governs concentration of the species. From a continuous-deterministic point of view, he derived rate equation for expected number of population of each species and from a discrete-stochastic point of view (by leveraging the probabilistic interpretation of amplitudes in quantum theory and using operators), he was able to obtain the underlying master equation. Then he made a connection between the state vector of the rate equation (classical state) and state vector of the master equation (mixed state) by averaging over probability distribution of the second one(amplitudes). Finally the author shows the required condition where both equations and formalism can be equivalent, which is large number limit and coherent regime. <p> <b>I am completely satisfied with this paper. Its a coherent and well-written paper with a new approach to reaction networks. This view may be of interest not only for researchers in this field but also for people in entire network society. I strongly recommend this paper for publication in this journal. </b> Besides, I have two questions for the author and I suggest him to rephrase these questions and add them as future works in the last part of the paper (Its up to the author to do this or not). <p> 1-Relation between rate equation and master equation has been discussed in the regime of the mass-action law. Does it work in other regimes? <p> 2-The author has derived the exact relation between rate equation formalism and master equation formalism when the initial state is a coherent state. Is it possible to have a non-coherent state which satisfy the equivalence condition (stated under the theorem 8)? </blockquote> Aargh! Emphasis mine: I've never gotten such a positive referee's report together with a rejection. I've asked some flunky at Springer to look into it, and I'll see what they have to say.
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66.
edited September 2018

31 December 2018:

Happy New Year!

Here is this week's progress, as far as I know:

1) Today Kenny and Daniel submitted a corrected version of their paper Spans of cospans in a topos to TAC. With luck it'll be published soon!

2) I finished the paper I'm writing with Blake, Joseph and John F: Network models. I think we're ready to put this on the arXiv and submit it to TAC.

The main thing left to do was give a more high-powered construction of symmetric monoidal categories from lax symmmetric monoidal functors F: C -> Cat using the theory of opfibrations and some 2-category theory. Christina kindly explained to us how to operate the necessary power tools!

3) On the negative progress front, when I asked the editor why my paper Quantum techniques for reaction networks from Natural Computing despite a positive referee's report, they said it was because the paper was too late for the special issue it was supposed to appear in. This was outrageous, given that the delays were all their fault. However, they said I could resubmit it after editing it.

Just for your amusement, here's how I replied:

Dear Joost Kok -

Thanks for the explanation! I would like to resubmit the paper right now, so it's attached below.

I first submitted this paper to Natural Computing on March 20, 2014. On January 26, 2016 I was told the manuscript was accepted but some corrections were required. The email didn't say what corrections were required. When I asked, I was told to wait for the editor to make a decision. On September 30, 2016 the guest editor, Ville Bergholm, told me:

We are writing to let you know that your paper is accepted, and is listed as accepted in the editorial system. Since this is a special issue, unfortunately we must wait until all the papers have completed the review process to complete publication.
On July 13, 2017, I got some referee's reports, and an unnamed editor told me:
Based on the advice received, I have decided that your manuscript can be accepted for publication after you have carried out the corrections as suggested by the reviewer(s).
I made the changes. On December 16th I got an email in which the referee said my paper deserved to be published... but the paper was rejected because the special issue has taken too long to appear.

I have never seen such a situation before. I hope you accept and actually publish my paper.

Best,
jb

I haven't heard back from him. I'll ask what's up in a week or two, when the holidays are over.

On the bright side, Lisa and I had a great time on a trip to the Navaho Nation in Arizona and then to Gallup, New Mexico. And, I've been having fun writing a series of blog articles about a 4-dimensional regular polytope with 600 tetrahedral faces:

Comment Source:31 December 2018: Happy New Year! Here is this week's progress, as far as I know: 1) Today Kenny and Daniel submitted a corrected version of their paper <a href = "https://arxiv.org/abs/1707.02098">Spans of cospans in a topos</a> to <i>TAC</i>. With luck it'll be published soon! 2) I finished the paper I'm writing with Blake, Joseph and John F: <a href = "https://arxiv.org/abs/1711.00037">Network models</a>. I think we're ready to put this on the arXiv and submit it to <i>TAC</i>. The main thing left to do was give a more high-powered construction of symmetric monoidal categories from lax symmmetric monoidal functors F: C -> Cat using the theory of opfibrations and some 2-category theory. Christina kindly explained to us how to operate the necessary power tools! 3) On the negative progress front, when I asked the editor why my paper <a href = "https://arxiv.org/abs/1306.3451">Quantum techniques for reaction networks</a> from <i>Natural Computing</i> despite a positive referee's report, they said it was because the paper was too late for the special issue it was supposed to appear in. This was outrageous, given that the delays were all their fault. However, they said I could resubmit it after editing it. Just for your amusement, here's how I replied: <blockquote> Dear Joost Kok - <p> Thanks for the explanation! I would like to resubmit the paper right now, so it's attached below. <p> I first submitted this paper to Natural Computing on March 20, 2014. On January 26, 2016 I was told the manuscript was accepted but some corrections were required. The email didn't say what corrections were required. When I asked, I was told to wait for the editor to make a decision. On September 30, 2016 the guest editor, Ville Bergholm, told me: <blockquote> We are writing to let you know that your paper is accepted, and is listed as accepted in the editorial system. Since this is a special issue, unfortunately we must wait until all the papers have completed the review process to complete publication. </blockquote> On July 13, 2017, I got some referee's reports, and an unnamed editor told me: <blockquote> Based on the advice received, I have decided that your manuscript can be accepted for publication after you have carried out the corrections as suggested by the reviewer(s). </blockquote> I made the changes. On December 16th I got an email in which the referee said my paper deserved to be published... but the paper was rejected because the special issue has taken too long to appear. <p> I have never seen such a situation before. I hope you accept and actually publish my paper. <p> Best,<br/> jb </blockquote> I haven't heard back from him. I'll ask what's up in a week or two, when the holidays are over. On the bright side, Lisa and I had a great time on a trip to the Navaho Nation in Arizona and then to Gallup, New Mexico. And, I've been having fun writing a series of blog articles about a 4-dimensional regular polytope with 600 tetrahedral faces: <ul> <li> <a href = "https://johncarlosbaez.wordpress.com/2017/12/16/the-600-cell/">The 600-cell (part 1)</a>. </li> <li> <a href = "https://johncarlosbaez.wordpress.com/2017/12/24/the-600-cell-part-2/">The 600-cell (part 2)</a>. </li> <li> <a href = "https://johncarlosbaez.wordpress.com/2017/12/28/the-600-cell-part-3/">The 600-cell (part 3)</a> </li> </ul> 
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67.
edited October 2018

6 January 2018:

Here is this week's progress, as far as I know:

1) Brandon will be doing a job interview for a visiting position at Colorado College! The interview will be at the Joint Mathematics Meetings in San Diego next week.

2) John Foley is giving at talk on Thursday at the Joint Mathematics Meetings!

• John Foley, Modeling the composition of networks with operads

Abstract. Networks can be combined in many ways including by overlaying one on top of another or sitting one next to another. We encode these two ways of combining networks as a specific kind of functor and prove that the application of a novel general construction to these functors results in typed operads. The class of operads we construct - which we call network operads - contains a wealth of examples whose many to one operations serve as a syntax for designing complex networks by composing simpler networks. We give examples of concrete ways to compose networks with our setup by matching specific kinds of networks to actions of network operads. Remarkably network operads can provide a unified treatment of the structural design and behavioral tasking of dynamic networks.

I guess some of you may miss our Wednesday meeting due to that conference. The rest of us should still have tons to talk about.

3) Daniel and Kenny's paper has appeared on TAC! As the saying goes, "the operad isn't over until the fat lady sings"... but now she has sung! View it in its full published beauty:

Abstract. For a topos T, there is a bicategory MonicSp(Csp(T)) whose objects are those of T, morphisms are cospans in T, and 2-morphisms are isomorphism classes of monic spans of cospans in T. Using a result of Shulman, we prove that MonicSp(Csp(T)) is symmetric monoidal, and moreover, that it is compact closed in the sense of Stay. We provide an application which illustrates how to encode double pushout rewrite rules as 2-morphisms inside a compact closed sub-bicategory of MonicSp(Csp(Graph)).

4) I invited Kathryn Hess and Steve Lack to join the advisory board of a new journal on applied category theory called Compositionality, and they accepted. Bob Coecke, Valeria de Paiva and I are also on the advisory board. It seems like the people actually doing the work to set up this journal are Brendan Fong, Nina Otter and Joshua Tan. A guy named Ilyas Khan of Cambridge Quantum Computing Inc. is providing the financial support - apparently he likes category theory!

This journal should start publishing around June, and this could be a good place to submit papers.

5) I got invited to speak at a conference called Symmetries, Observables, and the Noether's Theorems: A 100th Anniversary Conference for the Work of Emmy Noether at Fischer Hall in London Oct 5-6 2018. They asked me to speak about category-theoretic aspects of Noether's theorem on symmetries and conserved quantities. I may go, because I love Noether's theorem and this would give me an excuse to think about it harder. Plus, a bunch of cool people will be there. The ones I know are Yvette Kosmann-Schwarzbach, Harvey Brown, Jeremy Butterfield, Rob Spekkens, and Frank Wilczek (who won the Nobel prize for his work on confinement in quantum chromodynamics).

6) I got invited to speak at a workshop called Open Research: Rethinking Scientific Collaboration, which will be held at Perimeter Institute in Waterloo, Ontario on March 26-28, 2018. It sounds great; unfortunately I'll be busy.

7) I got invited to speak at a workshop with a very long title: Workshop on Higher Gauge Theory: Where should we look for higher gauge matter? (From emerging physics and topological quantum computing to string and M-theory), which is being held in Leeds, England on Feb. 28 - March 2. I'm not doing this stuff anymore so I won't go. Luckily my student John Huerta is going, and so is Urs Schreiber.

Christian Saemann will be there too: he recently used a categorified Lie algebra from my student Alissa Crans' thesis to make a concrete proposal for a mysterious 6-dimensional field theory that seems crucial for unifying M-theory, Khovanov homology and the geometric Langlands correspondence! I blogged about this here:

His proposal may not be right, but this is way-cool stuff.

8) I edited my paper Struggles with the continuum in accord with the referee's suggestions, and sent it back. I hope it's done, but I'm not sure.

Comment Source:6 January 2018: Here is this week's progress, as far as I know: 1) Brandon will be doing a job interview for a visiting position at Colorado College! The interview will be at the Joint Mathematics Meetings in San Diego next week. 2) John Foley is giving at talk on Thursday at the Joint Mathematics Meetings! * John Foley, Modeling the composition of networks with operads > **Abstract.** Networks can be combined in many ways including by overlaying one on top of another or sitting one next to another. We encode these two ways of combining networks as a specific kind of functor and prove that the application of a novel general construction to these functors results in typed operads. The class of operads we construct - which we call network operads - contains a wealth of examples whose many to one operations serve as a syntax for designing complex networks by composing simpler networks. We give examples of concrete ways to compose networks with our setup by matching specific kinds of networks to actions of network operads. Remarkably network operads can provide a unified treatment of the structural design and behavioral tasking of dynamic networks. I guess some of you may miss our Wednesday meeting due to that conference. The rest of us should still have tons to talk about. 3) Daniel and Kenny's paper has appeared on TAC! As the saying goes, "the operad isn't over until the fat lady sings"... but now she has sung! View it in its full published beauty: * Daniel Cicala and Kenny Courser, [Spans of cospans in a topos](http://www.tac.mta.ca/tac/volumes/33/1/33-01.pdf). > **Abstract.** For a topos T, there is a bicategory MonicSp(Csp(T)) whose objects are those of T, morphisms are cospans in T, and 2-morphisms are isomorphism classes of monic spans of cospans in T. Using a result of Shulman, we prove that MonicSp(Csp(T)) is symmetric monoidal, and moreover, that it is compact closed in the sense of Stay. We provide an application which illustrates how to encode double pushout rewrite rules as 2-morphisms inside a compact closed sub-bicategory of MonicSp(Csp(Graph)). 4) I invited Kathryn Hess and Steve Lack to join the advisory board of a new journal on applied category theory called Compositionality, and they accepted. Bob Coecke, Valeria de Paiva and I are also on the advisory board. It seems like the people actually doing the work to set up this journal are Brendan Fong, Nina Otter and Joshua Tan. A guy named [Ilyas Khan](http://cambridgequantum.com/team-ilyas-khan/) of Cambridge Quantum Computing Inc. is providing the financial support - apparently he likes category theory! This journal should start publishing around June, and this could be a good place to submit papers. 5) I got invited to speak at a conference called [Symmetries, Observables, and the Noether's Theorems: A 100th Anniversary Conference for the Work of Emmy Noether](https://philosophy.nd.edu/news/events/noether/) at Fischer Hall in London Oct 5-6 2018. They asked me to speak about category-theoretic aspects of Noether's theorem on symmetries and conserved quantities. I may go, because I love Noether's theorem and this would give me an excuse to think about it harder. Plus, a bunch of cool people will be there. The ones I know are Yvette Kosmann-Schwarzbach, Harvey Brown, Jeremy Butterfield, Rob Spekkens, and Frank Wilczek (who won the Nobel prize for his work on confinement in quantum chromodynamics). 6) I got invited to speak at a workshop called [Open Research: Rethinking Scientific Collaboration](https://www.perimeterinstitute.ca/conferences/open-research-rethinking-scientific-collaboration), which will be held at Perimeter Institute in Waterloo, Ontario on March 26-28, 2018. It sounds great; unfortunately I'll be busy. 7) I got invited to speak at a workshop with a very long title: [Workshop on Higher Gauge Theory: Where should we look for higher gauge matter? (From emerging physics and topological quantum computing to string and M-theory)](http://www1.maths.leeds.ac.uk/%7Eppmartin/SEMINARS/HGT_WS/index.html), which is being held in Leeds, England on Feb. 28 - March 2. I'm not doing this stuff anymore so I won't go. Luckily my student John Huerta is going, and so is Urs Schreiber. Christian Saemann will be there too: he recently used a categorified Lie algebra from my student Alissa Crans' thesis to make a concrete proposal for a mysterious 6-dimensional field theory that seems crucial for unifying M-theory, Khovanov homology and the geometric Langlands correspondence! I blogged about this here: * [An M5-brane model](https://golem.ph.utexas.edu/category/2017/12/an_m5brane_model.html). His proposal may not be right, but this is way-cool stuff. 8) I edited my paper [Struggles with the continuum](http://math.ucr.edu/home/baez/continuum.pdf) in accord with the referee's suggestions, and sent it back. I hope it's done, but I'm not sure.
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edited October 2018

20 January 2018:

I've got some good news and some bad news. First for the bad news:

1) My NSF proposal for getting money to send students to the Applied Category Theory conference in Leiden was rejected. So, right now, I don't know how to get any of you there.

Okay, now we need some good news.

2) My former student Mike Stay has a startup company called Pyrofex that's using serious category theory - like Graph-enriched Lawvere theories - to design distributed computing systems. Here is his news:

We just closed on a deal that makes my startup worth millions! :D

It's all just on paper at the moment: because one party paid a certain amount for shares of stock, we can claim that the rest of the shares have the same price. Similarly, we did a token swap, which essentially makes the rest of our tokens be "worth" as much as theirs. So if someone wanted to buy us, we'd have a good argument for why they should pay us millions. Now we have to work hard for the next year to meet our obligations and turn these tokens into liquid assets.

In the meantime, next month I get a salary that's about half of what I was earning at Google instead of the third I've been living on for a couple of years. Hooray!

Here is a more formal announcement. Christian Williams should be especially interested, since it involves blockchain technology:

8 January 2018 — The RChain Cooperative and Pyrofex Corporation today announced strategically important service contracts and an equity investment intended to deliver several mutually beneficial blockchain solutions. RChain will acquire 1.1 million shares of Pyrofex Common Stock as a strategic investment. The two companies will ink separate service contracts to reinforce their existing relationship and help to align their business interests.

Pyrofex will develop critical tools and platform components necessary for the long-term success of the RChain platform. These tools are designed to leverage RChain’s unique blockchain environment and make blockchain development simpler, faster, and more effective than ever before. Under these agreements, Pyrofex will develop the world’s first decentralized IDE for writing blockchain smart contracts on the RChain blockchain.

Pyrofex also commits to continuing the core development of RChain’s blockchain platform and to organizing RChain’s global developer events and conferences.

“We’re thrilled to have an opportunity to strengthen our relationship with the RChain Cooperative in 2018. Their commitment to open-source development mirrors our own corporate values. It’s a pleasure to have such a close relationship with a vibrant open-source community. I’ve rarely seen the kind of excitement the Coop’s members share and we look forward to delivering some great new technology this year.” — Nash E. Foster, Cofounder & CEO, Pyrofex Corp.

“Intuitive development tools are important for us and the blockchain ecosystem as a whole; we’re incredibly glad Pyrofex intends to launch their tools on RChain first. But, Ethereum has been a huge supporter of RChain and we’re pleased that Pyrofex intends to support Solidity developers as well. Having tools that will make it possible for developers to migrate smart contracts between blockchains is going to create tremendous possibilities.” — Lucius Greg Meredith, President, RChain Cooperative Background

Pyrofex is a software development company co-founded by Dr. Michael Stay, PhD and Nash Foster in 2016. Dr. Stay and Greg Meredith are long-time colleagues and collaborators whose mutual research efforts form the mathematical foundations of RChain’s technology. One example of the work that Greg and Mike have collaborated on is the work on the LADL (Logic as Distributed Law) algorithm. You can watch Dr. Stay present the latest research from the RChain Developers retreat.

Pyrofex and its development team should be familiar to those who follow the RChain Cooperative. They currently employ 14 full-time and several part-time developers dedicated to RChain platform development. Pyrofex CEO Nash Foster and Lead Project Manager Medha Parlikar have helped grow RChain’s development team to an impressive 20+ Core devs with plans on doubling by mid 2018. The team now includes multiple PhDs, ex-Googlers, and other word class talents.

There are more technical details further down the page I got this from:

http://coin5s.com/content/rchain-cooperative-pyrofex-corporation-announce-strategic-partnership

Comment Source:20 January 2018: I've got some good news and some bad news. First for the bad news: 1) My NSF proposal for getting money to send students to the Applied Category Theory conference in Leiden was rejected. So, right now, I don't know how to get any of you there. Okay, now we need some good news. 2) My former student Mike Stay has a startup company called Pyrofex that's using serious category theory - like Graph-enriched Lawvere theories - to design distributed computing systems. Here is his news: > We just closed on a deal that makes my startup worth millions! :D > It's all just on paper at the moment: because one party paid a certain amount for shares of stock, we can claim that the rest of the shares have the same price. Similarly, we did a token swap, which essentially makes the rest of our tokens be "worth" as much as theirs. So if someone wanted to buy us, we'd have a good argument for why they should pay us millions. Now we have to work hard for the next year to meet our obligations and turn these tokens into liquid assets. > In the meantime, next month I get a salary that's about half of what I was earning at Google instead of the third I've been living on for a couple of years. Hooray! Here is a more formal announcement. Christian Williams should be especially interested, since it involves blockchain technology: > 8 January 2018 — The RChain Cooperative and Pyrofex Corporation today announced strategically important service contracts and an equity investment intended to deliver several mutually beneficial blockchain solutions. RChain will acquire 1.1 million shares of Pyrofex Common Stock as a strategic investment. The two companies will ink separate service contracts to reinforce their existing relationship and help to align their business interests. > Pyrofex will develop critical tools and platform components necessary for the long-term success of the RChain platform. These tools are designed to leverage RChain’s unique blockchain environment and make blockchain development simpler, faster, and more effective than ever before. Under these agreements, Pyrofex will develop the world’s first decentralized IDE for writing blockchain smart contracts on the RChain blockchain. > Pyrofex also commits to continuing the core development of RChain’s blockchain platform and to organizing RChain’s global developer events and conferences. > **Comments on the News** > “We’re thrilled to have an opportunity to strengthen our relationship with the RChain Cooperative in 2018. Their commitment to open-source development mirrors our own corporate values. It’s a pleasure to have such a close relationship with a vibrant open-source community. I’ve rarely seen the kind of excitement the Coop’s members share and we look forward to delivering some great new technology this year.” — Nash E. Foster, Cofounder & CEO, Pyrofex Corp. > “Intuitive development tools are important for us and the blockchain ecosystem as a whole; we’re incredibly glad Pyrofex intends to launch their tools on RChain first. But, Ethereum has been a huge supporter of RChain and we’re pleased that Pyrofex intends to support Solidity developers as well. Having tools that will make it possible for developers to migrate smart contracts between blockchains is going to create tremendous possibilities.” — Lucius Greg Meredith, President, RChain Cooperative Background > Pyrofex is a software development company co-founded by Dr. Michael Stay, PhD and Nash Foster in 2016. Dr. Stay and Greg Meredith are long-time colleagues and collaborators whose mutual research efforts form the mathematical foundations of RChain’s technology. One example of the work that Greg and Mike have collaborated on is the work on the LADL (Logic as Distributed Law) algorithm. You can watch Dr. Stay present the latest research from the RChain Developers retreat. > Pyrofex and its development team should be familiar to those who follow the RChain Cooperative. They currently employ 14 full-time and several part-time developers dedicated to RChain platform development. Pyrofex CEO Nash Foster and Lead Project Manager Medha Parlikar have helped grow RChain’s development team to an impressive 20+ Core devs with plans on doubling by mid 2018. The team now includes multiple PhDs, ex-Googlers, and other word class talents. There are more technical details further down the page I got this from: [http://coin5s.com/content/rchain-cooperative-pyrofex-corporation-announce-strategic-partnership](http://coin5s.com/content/rchain-cooperative-pyrofex-corporation-announce-strategic-partnership) 
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Thank you

Comment Source:Thank you
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edited October 2018

24 January 2018:

After a slow stretch and some bad news, progress proceeds:

1) Nina Otter got not just one but two postdoc positions!

She got a 3-year offer at UCLA, and also an offer for a postdoc at the Max Planck Institute in Leipzig, Germany. She liked both these offers, so she spent the last two weeks doing negotiations. The upshot is that she'll officially start in both places this summer. But she doesn't need to teach at UCLA in the summer, and she'll take a leave during the fall, so she'll work in Leipzig then and actually move to Los Angeles in January 2019. She plans to spend future summers at Leipzig, and be at UCLA during the school year.

At UCLA she'll will be working with Guido Montufar and Mason Porter, on theoretical foundations for machine learning (with Montufar) and networks (with Porter). They'll try to combine existing approaches with new approaches using topological data analysis, category theory, and algebraic geometry. At the Max Planck Institute she'll be working with Jürgen Jost and Bernd Sturmfels. Both are great mathematician/scientists.

Congratulations, Nina!

2) Christian Williams has written a good overview of the first Statebox Summit:

I first met the young Dutch hacktivist Jelle Herold at a meeting on network theory that I helped run in Torino. I saw him again at a Simons Institute meeting on compositionality in computer science. He was already talking about his new startup.

Now it’s here. It’s called Statebox. Among other things, it’s an ambitious attempt to combine categories, open games, dependent types, Petri nets, string diagrams, and blockchains into a universal language for distributed systems.

Herold is inviting academics to help. I want to. But I couldn’t go to the Croatian island of Zlarin at the drop of a hat during classes. Luckily, Christian is fascinated by the idea of using category theory and blockchain technology to do something good for the world! So, I sent him to the first Statebox summit as my "deputy", and this is his report.

3) People at the Adjoint School associated to ACT2018 are starting to write blog articles on the papers they're reading, and Joseph Moeller wrote the first, along with Dmitri Vagner:

There's even more, but I'll save it for next time.

Comment Source:24 January 2018: After a slow stretch and some bad news, progress proceeds: 1) Nina Otter got not just one but two postdoc positions! She got a 3-year offer at UCLA, and also an offer for a postdoc at the Max Planck Institute in Leipzig, Germany. She liked both these offers, so she spent the last two weeks doing negotiations. The upshot is that she'll officially start in both places this summer. But she doesn't need to teach at UCLA in the summer, and she'll take a leave during the fall, so she'll work in Leipzig then and actually move to Los Angeles in January 2019. She plans to spend future summers at Leipzig, and be at UCLA during the school year. At UCLA she'll will be working with Guido Montufar and Mason Porter, on theoretical foundations for machine learning (with Montufar) and networks (with Porter). They'll try to combine existing approaches with new approaches using topological data analysis, category theory, and algebraic geometry. At the Max Planck Institute she'll be working with Jürgen Jost and Bernd Sturmfels. Both are great mathematician/scientists. Congratulations, Nina! 2) Christian Williams has written a good overview of the first Statebox Summit: * Christian Williams, [Statebox: a universal language of distributed systems](https://johncarlosbaez.wordpress.com/2018/01/22/statebox-a-universal-language-of-distributed-systems/), Azimuth, January 22, 2018. I first met the young Dutch hacktivist Jelle Herold at a meeting on network theory that I helped run in Torino. I saw him again at a Simons Institute meeting on compositionality in computer science. He was already talking about his new startup. Now it’s here. It’s called Statebox. Among other things, it’s an ambitious attempt to combine categories, open games, dependent types, Petri nets, string diagrams, and blockchains into a universal language for distributed systems. Herold is inviting academics to help. I want to. But I couldn’t go to the Croatian island of Zlarin at the drop of a hat during classes. Luckily, Christian is fascinated by the idea of using category theory and blockchain technology to do something good for the world! So, I sent him to the first Statebox summit as my "deputy", and this is his report. 3) People at the Adjoint School associated to ACT2018 are starting to write blog articles on the papers they're reading, and Joseph Moeller wrote the first, along with Dmitri Vagner: * Joseph Moeller and Dmitri Vagner, [A categorical semantics for causal structure](https://golem.ph.utexas.edu/category/2018/01/a_categorical_semantics_for_ca.html), The n-Category Caf&eacute;, January 22, 2018. There's even more, but I'll save it for next time.
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edited October 2018

1 February 2018:

1) Today this paper by Daniel Cicala was published in TAC!

Abstract. We study spans of cospans in a category C and explain how to horizontally and vertically compose these. When C is a topos and the legs of the spans are monic, these two forms of composition satisfy the interchange law. In this case there is a bicategory of objects, cospans, and monic-legged' spans of cospans in C. One motivation for this construction is an application to graph rewriting.

2) Blake Pollard has applied for a 2-year National Research Council fellowship at the place he's already working now, the National Institute of Standards and Technology.

3) Blake also applied to Google's AI Residency Program.

Some of you may, someday, want to follow suit and apply for these yourselves!

4) Brandon and I dealt with the referee's comments on our paper Props in network theory and resubmitted it to Tom Leinster at TAC. It will now go to a second referee who knows more about category theory and probably less about symplectic geometry and electrical engineering.

The first referee had a lot of useful specific comments which I won't show you, but he began with some very negative general comments which I will show you, just so you know that you've got to be tough: don't give up when a referee hates your paper!

Here are the first referee's comments:

The manuscript under review appears to be a part of a program of John Baez and his collaborators to understand networks of various kinds in terms of morphisms of symmetric monoidal categories. It seems that the main result is an extension of the black-boxing theorem of Baez and Fong, Theorem 49. The authors never explicitly state what the main result of the paper actually is.

I wish the authors had spent more time explaining what they are doing and why. Having an actual example of the black-boxing functor applied to a circuit would have been useful as well as well. (While the paper contains paragraphs labeled as "example" they are really constructions and short propositions and not really illustrative examples.) There are hints in the paper scattered here and there that the results should have applica- tions in engineering either as mathematical models of the bond graph formalism or as a new mathematical approach to the behavioral point of view of systems as advocated by Willems. Unfortunately the authors never explicitly engage with the current bond graph literature. In particular the authors ignore (or are unaware of?) port-Hamiltonian systems, a popular modern version of the bond graph formalism. Willems is mentioned briefly (not by name): "In general, engineers have found the relation between electrical circuits and signal-flow diagrams rather problematic [44]." Having called engineers stupid the authors fail to explained why their approach is superior.

I am put off by the style of writing. The paper reads like a series of blog posts where a reader is invited to come along on a long and interesting journey with a number of side trips. Easy things are explained at length while harder arguments are swept under the rug or left vague or put in an appendix. There are white lies scattered here and there which are not entirely benign. It is never clear what audience the authors are writing for.

To conclude: the paper is too long, unfocused and unclear. It needs to be re-written and in particular, shortened, before it could be considered for publication in TAC.

Luckily Tom Leinster realize that the first referee was being a bit unreasonable, in particular by saying

I wish the authors had spent more time explaining what they are doing and why

and also

the paper is too long... It needs to be re-written and in particular, shortened

So, he's giving us a second chance with another referee. Bruised but not defeated, we live on to fight another day!

Comment Source:1 February 2018: 1) Today this paper by Daniel Cicala was published in TAC! * Daniel Cicala, [Spans of cospans](http://www.tac.mta.ca/tac/volumes/33/6/33-06abs.html). <blockquote><b>Abstract.</b> We study spans of cospans in a category C and explain how to horizontally and vertically compose these. When C is a topos and the legs of the spans are monic, these two forms of composition satisfy the interchange law. In this case there is a bicategory of objects, cospans, and monic-legged' spans of cospans in C. One motivation for this construction is an application to graph rewriting. </blockquote> 2) Blake Pollard has applied for a 2-year <a href = "http://sites.nationalacademies.org/pga/rap/">National Research Council</a> fellowship at the place he's already working now, the National Institute of Standards and Technology. 3) Blake also applied to Google's <a href = "https://research.google.com/teams/brain/residency/">AI Residency Program</a>. Some of you may, someday, want to follow suit and apply for these yourselves! 4) Brandon and I dealt with the referee's comments on our paper Props in network theory and resubmitted it to Tom Leinster at TAC. It will now go to a second referee who knows more about category theory and probably less about symplectic geometry and electrical engineering. The first referee had a lot of useful specific comments which I won't show you, but he began with some very negative general comments which I will show you, just so you know that you've got to be tough: don't give up when a referee hates your paper! Here are the first referee's comments: <blockquote> The manuscript under review appears to be a part of a program of John Baez and his collaborators to understand networks of various kinds in terms of morphisms of symmetric monoidal categories. It seems that the main result is an extension of the black-boxing theorem of Baez and Fong, Theorem 49. The authors never explicitly state what the main result of the paper actually is. <p> I wish the authors had spent more time explaining what they are doing and why. Having an actual example of the black-boxing functor applied to a circuit would have been useful as well as well. (While the paper contains paragraphs labeled as "example" they are really constructions and short propositions and not really illustrative examples.) There are hints in the paper scattered here and there that the results should have applica- tions in engineering either as mathematical models of the bond graph formalism or as a new mathematical approach to the behavioral point of view of systems as advocated by Willems. Unfortunately the authors never explicitly engage with the current bond graph literature. In particular the authors ignore (or are unaware of?) port-Hamiltonian systems, a popular modern version of the bond graph formalism. Willems is mentioned briefly (not by name): "In general, engineers have found the relation between electrical circuits and signal-flow diagrams rather problematic [44]." Having called engineers stupid the authors fail to explained why their approach is superior. <p> I am put off by the style of writing. The paper reads like a series of blog posts where a reader is invited to come along on a long and interesting journey with a number of side trips. Easy things are explained at length while harder arguments are swept under the rug or left vague or put in an appendix. There are white lies scattered here and there which are not entirely benign. It is never clear what audience the authors are writing for. <p> To conclude: the paper is too long, unfocused and unclear. It needs to be re-written and in particular, shortened, before it could be considered for publication in TAC. </blockquote> Luckily Tom Leinster realize that the first referee was being a bit unreasonable, in particular by saying <blockquote> I wish the authors had spent more time explaining what they are doing and why </blockquote> and also <blockquote> the paper is too long... It needs to be re-written and in particular, shortened </blockquote> So, he's giving us a second chance with another referee. Bruised but not defeated, we live on to fight another day!
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9 February 2018:

This week's progress:

1) Adam Yassine was accepted to a Mathematical Sciences Research Institute workshop called "From Symplectic Geometry to Chaos". It runs from July 23rd to August 3rd this summer. This is great because he's working on symplectic geometry and open classical systems! He should take advantage of this opportunity to check out Berkeley and visit their math department.

2) As part of the Applied Category Theory school, Joseph Moeller wrote a blog article on the n-Category Cafe:

3) Also for this school, Jade Master wrote this blog article:

It's really fun reading these articles and thinking about more ways to use categories!

4) Mike Stay has hired Christian Williams and me to do some research for his startup Pyrofex. I'm very excited about this. We'll probably start by working on ideas that can already be found here:

• John Baez, Pyrofex, Azimuth, February 4, 2018.

5) John Paschkewitz of DARPA has agreed to pay for me to speak at the Applied Category Theory conference at the National Institute of Standards in March.

That's where Blake is working now.... with the guy who is running this conference, Spencer Breiner!

Comment Source:9 February 2018: This week's progress: 1) Adam Yassine was accepted to a Mathematical Sciences Research Institute workshop called "From Symplectic Geometry to Chaos". It runs from July 23rd to August 3rd this summer. This is great because he's working on symplectic geometry and open classical systems! He should take advantage of this opportunity to check out Berkeley and visit their math department. 2) As part of the Applied Category Theory school, Joseph Moeller wrote a blog article on the n-Category Cafe: * Joe Moeller, <a href = "https://golem.ph.utexas.edu/category/2018/01/a_categorical_semantics_for_ca.html">A categorical semantics for causal structure</a>, The n-Category Caf&eacute;, January 22, 2018. 3) Also for this school, Jade Master wrote this blog article: * Jade Master, <a href = "https://golem.ph.utexas.edu/category/2018/02/linguistics_using_category_the.html">Linguistics using category theory</a>, The n-Category Caf&eacute;, February 6, 2018. It's really fun reading these articles and thinking about more ways to use categories! 4) Mike Stay has hired Christian Williams and me to do some research for his startup Pyrofex. I'm very excited about this. We'll probably start by working on ideas that can already be found here: * Michael Stay and Lucius Gregory Meredith, <a href = "https://arxiv.org/abs/1704.03080">Representing operational semantics with enriched Lawvere theories</a>. If your curious, I blogged about some of these things here: * John Baez, <a href = "https://johncarlosbaez.wordpress.com/2018/02/04/pyrofex/">Pyrofex</a>, Azimuth, February 4, 2018. 5) John Paschkewitz of DARPA has agreed to pay for me to speak at the Applied Category Theory conference at the National Institute of Standards in March. That's where Blake is working now.... with the guy who is running this conference, Spencer Breiner!
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19 February 2018:

I don't know much that was completed this week, but:

1) I sent the math department chair, Poon, an email requesting funds for 3 grad students to attend Applied Category Theory 2018. I'm estimating $1000 for air fare and$1300 for lodging for each student. He will probably try to bargain me down in various ways, including the number of students.

2) On Wednesday at noon Helen Chen is going to visit us. She's a "grants facilitator" at UCR. Poon asked her to help me find some grants, given the failure of my NSF proposal to get money for ACT2018.

3) The Metron gang asked me to write a blog article summarizing my work with John Foley and Joe Moeller on operads for system design, so I did that:

This explains for the first time a bit about our work on compositional tasking using graphic monoids. Those of you reading Lawvere's paper on graphic monoids might like to see this! Once Joe finishes his paper on "Functorial network models", we should write a paper about this.

Comment Source:19 February 2018: I don't know much that was completed this week, but: 1) I sent the math department chair, Poon, an email requesting funds for 3 grad students to attend Applied Category Theory 2018. I'm estimating $1000 for air fare and$1300 for lodging for each student. He will probably try to bargain me down in various ways, including the number of students. 2) On Wednesday at noon Helen Chen is going to visit us. She's a "grants facilitator" at UCR. Poon asked her to help me find some grants, given the failure of my NSF proposal to get money for ACT2018. 3) The Metron gang asked me to write a blog article summarizing my work with John Foley and Joe Moeller on operads for system design, so I did that: * John Baez, <a href = "https://johncarlosbaez.wordpress.com/2018/02/19/complex-adaptive-systems-part-7/">Complex Adaptive System Design (Part 7)</a>, Azimuth, February 19, 2018. This explains for the first time a bit about our work on compositional tasking using graphic monoids. Those of you reading Lawvere's paper on graphic monoids might like to see this! Once Joe finishes his paper on "Functorial network models", we should write a paper about this. 
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74.

25 February 2018:

1) Poon offered Daniel, Jade and Joseph $1000 each to attend Applied Category Theory 2018. Brendan offered them additional funds. I believe all three have now bought airplane tickets for this event - both the school (April 23-27) and the ensuing workshop (April 30-May 4). I hope all three know how long it takes to get or renew a passport - if you start now you may not be done in time unless you pay for expedited service. 2) Daniel wrote a blog article as part of the lead-up to this school: This is nice because some bicategories that Daniel is studying, with rewrites as 2-morphisms, are "cartesian" in this sense. The classic example is [sets, relations, implications], where the relation R from X to Y implies the relation S if R ⊆ S ⊆ X x Y. 3) I submitted a proposal to Mario Rasetti to set up a mathematics research group at the Institute of Scientific Interchange in Torino, Italy. You may recall that he invited me to do this last summer. For a while I didn't have enough energy. I now realize that came from a combination of Trump's madness, my mother's death, and the hassle of selling her estate. I'm feeling more peppy these days! Comment Source:25 February 2018: 1) Poon offered Daniel, Jade and Joseph$1000 each to attend Applied Category Theory 2018. Brendan offered them additional funds. I believe all three have now bought airplane tickets for this event - both the <a href = "https://johncarlosbaez.wordpress.com/2017/10/22/applied-category-theory-2018-adjoint-school/">school</a> (April 23-27) and the ensuing <a href = "https://johncarlosbaez.wordpress.com/2017/09/12/act-2018/">workshop</a> (April 30-May 4). I hope all three know how long it takes to get or renew a passport - if you start now you may not be done in time unless you pay for expedited service. 2) Daniel wrote a blog article as part of the lead-up to this school: * Daniel Cicala and Jules Hedges, <a href = "https://golem.ph.utexas.edu/category/2018/02/cartesian_bicategories.html">Cartesian bicategories</a>, February 19, 2018. This is nice because some bicategories that Daniel is studying, with rewrites as 2-morphisms, are "cartesian" in this sense. The classic example is [sets, relations, implications], where the relation R from X to Y implies the relation S if R ⊆ S ⊆ X x Y. 3) I submitted a proposal to <a href = "https://www.isi.it/en/people/mario-rasetti">Mario Rasetti</a> to set up a mathematics research group at the <a href = "https://www.isi.it/en/home">Institute of Scientific Interchange</a> in Torino, Italy. You may recall that he invited me to do this last summer. For a while I didn't have enough energy. I now realize that came from a combination of Trump's madness, my mother's death, and the hassle of selling her estate. I'm feeling more peppy these days!
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3 March 2018:

1) I posted another blog article written by students at the ACT2018 school:

This is a nice introduction to Brendan's theory of decorated cospans.

2) Kenny Courser and I are close to finishing a paper - close enough that I blogged about it to ask for comments and corrections:

You can get the paper from here. If any of you can look through it and find mistakes or things that are hard to understand, please let me know!

3) Christian Williams and I signed contracts to work for Pyrofex, and we had our first conversation with Mike Stay about this project. We'll start by working on ideas in here:

This project should be fun, because it'll connect network theory with computer science... and Mike and Greg actually know a bunch of computer science.

Finally, not really relevant to our grand scheme: I took a little break today by blogging about mathematical logic:

Briefly: if you start with a nonstandard model of the natural numbers, you can define integers in the usual way (as differences of your nonstandard natural numbers), and then rational numbers (as ratios of integers). So, there are lots of nonstandard versions of the rational numbers! Any one of these gives a field. Now for the cool part: if your nonstandard model of the natural numbers is countable, your field of nonstandard rational numbers can be seen as a subfield of the ordinary complex numbers! This is counterintuitive at first, because we tend to think of nonstandard models of Peano arithmetic as spooky and elusive things, while we tend to think of the complex numbers as well-understood. But I explain why it makes sense.

Comment Source:3 March 2018: 1) I posted another blog article written by students at the ACT2018 school: * Jonathan Lorand and Fabrizio Genovese, <a href = "https://golem.ph.utexas.edu/category/2018/02/hypergraph_categories_of_cospa.html">Hypergraph categories of cospans</a>, The n-Category Caf&eacute, February 28, 2018. This is a nice introduction to Brendan's theory of decorated cospans. 2) Kenny Courser and I are close to finishing a paper - close enough that I blogged about it to ask for comments and corrections: * John Baez, Coarse-graining open Markov processes, <a href = "https://golem.ph.utexas.edu/category/2018/03/coarsegraining_open_markov_pro.html">The n-Category Caf&eacute;</a>, March 4, 2018. You can get the paper from here. If any of you can look through it and find mistakes or things that are hard to understand, please let me know! 3) Christian Williams and I signed contracts to work for Pyrofex, and we had our first conversation with Mike Stay about this project. We'll start by working on ideas in here: * Mike Stay and Greg Meredith, <a href = "https://arxiv.org/abs/1704.03080">Representing operational semantics with graph-enriched Lawvere theories</a>. This project should be fun, because it'll connect network theory with computer science... and Mike and Greg actually know a bunch of computer science. Finally, not really relevant to our grand scheme: I took a little break today by blogging about mathematical logic: * John Baez, <a href = "https://johncarlosbaez.wordpress.com/2018/03/03/nonstandard-integers-as-complex-numbers/">Nonstandard integers as complex numbers</a>, Azimuth, March 3, 2018. Briefly: if you start with a nonstandard model of the natural numbers, you can define integers in the usual way (as differences of your nonstandard natural numbers), and then rational numbers (as ratios of integers). So, there are lots of nonstandard versions of the rational numbers! Any one of these gives a field. Now for the cool part: if your nonstandard model of the natural numbers is countable, your field of nonstandard rational numbers can be seen as a subfield of the ordinary complex numbers! This is counterintuitive at first, because we tend to think of nonstandard models of Peano arithmetic as spooky and elusive things, while we tend to think of the complex numbers as well-understood. But I explain why it makes sense.
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12 March 2018:

This week's progress:

1) I posted another blog article by ACT2018 students - a second one on linguistics and category theory:

I love the category of convex sets, which has deep connections to information theory, so this is exciting to me.

2) Kenny and I finished this paper, put it on the arXiv, and submitted it to Theory and Applications of Categories:

I submitted it to Kathryn Hess, one of the editors who we haven't already worn out with our papers. Luckily I know a lot of editors at this journal - she was a grad student at MIT studying homotopy when I was hanging around there while teaching at Wellesley College for two years.

By the way, Brendan is hard at work on a book on applications of category theory with David Spivak. I hope he lets us know when it reaches some stage of being done... like hitting the arXiv.

Comment Source:12 March 2018: This week's progress: 1) I posted another blog article by ACT2018 students - a second one on linguistics and category theory: * Tai-Danae Bradley and Brad Theilman, <a href = "https://golem.ph.utexas.edu/category/2018/03/cognition_convexity_and_catego.html">Cognition, convexity and category theory</a>. I love the category of convex sets, which has deep connections to information theory, so this is exciting to me. 2) Kenny and I finished this paper, put it on the arXiv, and submitted it to Theory and Applications of Categories: * John Baez and Kenny Courser, <a href = "https://arxiv.org/abs/1710.11343">Coarse-graining open Markov processes</a>. I submitted it to Kathryn Hess, one of the editors who we haven't already worn out with our papers. Luckily I know a lot of editors at this journal - she was a grad student at MIT studying homotopy when I was hanging around there while teaching at Wellesley College for two years. By the way, Brendan is hard at work on a book on applications of category theory with David Spivak. I hope he lets us know when it reaches some stage of being done... like hitting the arXiv.
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edited November 2018

20 March 2018:

This week's progress:

1) Brendan came out with a new book:

Abstract. This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed.

It looks great, and I should blog about it!

2) Brendan and David announced their book at last week's applied category theory workshop at NIST. And a lot of other things happened at this workshop! Too many to list, since there were about 17 academics there, half category theorists, and also about 15 folks from industry and about 11 from government. It was focused more on networking and less on technical details:

• I caught up with Blake, who is working at NIST using Spivak's Algebraic Query Language to help design better power grids - a massive extension of my work with Brendan on categories and electrical circuits.
• I talked to Brendan, Joshua Tan and Bob Coecke about the new applied category theory journal Compositionality. We're all either editors or on the advisory board, and we signed the new constitution of this journal, which will start up this summer.
• I talked to Jelle Herold and Fabrizio Genovese about Statebox, Jelle's new startup that's using Petri nets and blockchain technology and other things to provide businesses with better supply chain management and the like. Jelle focused on one application: the cobalt mining industry! I always enjoy talking to him.
• Andrew Vlasic of the Army Research Office said he is funding work on stochastic dynamics and we should apply for funding by sending him a 1.5 page "white paper" that talks about insufficiencies in existing work. He also said he can fund conferences for up to $20,000. • Jared Culbertson of the Air Force Research Lab in Dayton Ohio said he has postdoc funding for category theory and dynamical systems. I see he's written a paper A categorical foundation for Bayesian probability, which sounds like something Brendan and Daniel should know about. • Steve Huntsman of BAE systems says they "love interns", as did Arquimedes Canedo of Siemens (who took on Blake as an intern last summer). So, I think you guys should apply for summer internships! I'm gonna pressure you to give it a try. Even if you want to go into academia, this will look good on your resume - and show you an alternative path forward. I was impressed by how many people said they got into applied category theory by reading the Rosetta Stone paper that Mike Stay and I wrote... and how many read my blog Azimuth. In short, applied category theory seems to be taking off! You can read more about this workshop here: The comments discuss some of the talks. Comment Source:20 March 2018: This week's progress: 1) Brendan came out with a new book: * Brendan Fong and David I. Spivak, <i><a href = "https://arxiv.org/abs/1803.05316">Seven Sketches in Compositionality: An Invitation to Applied Category Theory</a></i>. > <b>Abstract</b>. This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed. It looks great, and I should blog about it! 2) Brendan and David announced their book at last week's applied category theory workshop at NIST. And a lot of other things happened at this workshop! Too many to list, since there were about 17 academics there, half category theorists, and also about 15 folks from industry and about 11 from government. It was focused more on networking and less on technical details: <ul> <li>I caught up with Blake, who is working at NIST using Spivak's Algebraic Query Language to help design better power grids - a massive extension of my work with Brendan on categories and electrical circuits. </li> <li>I talked to Brendan, Joshua Tan and Bob Coecke about the new applied category theory journal Compositionality. We're all either editors or on the advisory board, and we signed the new constitution of this journal, which will start up this summer. </li> <li> I talked to Jelle Herold and Fabrizio Genovese about <a href = "https://johncarlosbaez.wordpress.com/2018/01/22/statebox-a-universal-language-of-distributed-systems/">Statebox</a>, Jelle's new startup that's using Petri nets and blockchain technology and other things to provide businesses with better supply chain management and the like. Jelle focused on one application: the cobalt mining industry! I always enjoy talking to him. </li> <li> <a href = "https://www.linkedin.com/in/andrew-vlasic-03872499">Andrew Vlasic of the Army Research Office</a> said he is funding work on stochastic dynamics and we should apply for funding by sending him a 1.5 page "white paper" that talks about insufficiencies in existing work. He also said he can fund conferences for up to$20,000. </li> <li> Jared Culbertson of the Air Force Research Lab in Dayton Ohio said he has <a href = "http://www.appliedcategorytheory.org/postdoc-position-at-air-force-research-laboratory-afrl/">postdoc funding</a> for category theory and dynamical systems. I see he's written a paper <a href = "https://arxiv.org/abs/1205.1488">A categorical foundation for Bayesian probability</a>, which sounds like something Brendan and Daniel should know about. </li> <li> Steve Huntsman of BAE systems says they "love interns", as did Arquimedes Canedo of Siemens (who took on Blake as an intern last summer). So, I think you guys should apply for summer internships! I'm gonna pressure you to give it a try. Even if you want to go into academia, this will look good on your resume - and show you an alternative path forward. </li> </ul> I was impressed by how many people said they got into applied category theory by reading the Rosetta Stone paper that Mike Stay and I wrote... and how many read my blog Azimuth. In short, applied category theory seems to be taking off! You can read more about this workshop here: <ul> <li>John Baez, <a href = "https://johncarlosbaez.wordpress.com/2018/02/17/applied-category-theory-at-nist/">Applied category theory at NIST (part 1)</a>, <i>Azimuth</i>, 17 February 2018. </li> </ul> The comments discuss some of the talks.
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edited November 2018

25 March 2018:

This week:

1) I decided to run an online seminar on applied category theory based on Brendan's new book. This spring I won't be on campus much, and this summer even less, so I urge all you students to register for this seminar! Details are here:

It will start slowly and gently.

2) Nash Foster invited Christian Williams and me to attend the RChain Spring Dev Conference in Boulder Colorado from April 17th to 18th. I can't attend but Christian will.

In case you're not keeping track: Nash Foster and my former student Mike Stay are running a company called, but they're working closely with RChain, run by Mike's friend Greg Meredith. Both these companies use a lot of math, like category theory. Christian and I are now being paid by Pyrofex to write papers; our first will be on enriched categories for operational semantics.

Mike and Greg recently went on a European tour, talking a lot of top experts in category theory and computer science, offering them research grants to work with RChain. A bunch of these top experts are friends of mine, so this is pretty exciting.

3) I got contacted by Sam Stanton, who runs a research program on Complex Dynamics and Systems at the Army Research Office. He asked if I'd like to talk about funding and I said yes. This program seems right up my alley - here's the description:

The Complex Dynamics and Systems Program emphasizes fundamental understanding of the dynamics, both physical and information theoretic, of nonlinear and nonconservative systems as well as innovative scientific approaches for engineering and exploiting nonlinear and nonequilibrium physical and information theoretic dynamics for a broad range of future capabilities (e.g. novel energetic and entropic transduction, agile motion, and force generation). A common theme amongst all programmatic thrust areas is that systems of interest are "open" in the thermodynamic sense (or, similarly, dissipative dynamical systems).

I haven't heard back from him yet; he was busy at a conference this week. But I'm optimistic.

Comment Source:25 March 2018: This week: 1) I decided to run an online seminar on applied category theory based on Brendan's new book. This spring I won't be on campus much, and this summer even less, so I urge all you students to register for this seminar! Details are here: <ul> <li> John Baez, <a href = "https://johncarlosbaez.wordpress.com/2018/03/26/seven-sketches-in-compositionality/">Applied Category Theory - Online Course</a>, <i>Azimuth</i>, 26 March 2018. </li> </ul> It will start slowly and gently. 2) Nash Foster invited Christian Williams and me to attend the <a href = "https://developer.rchain.coop/rchain-developer-conference.pdf">RChain Spring Dev Conference</a> in Boulder Colorado from April 17th to 18th. I can't attend but Christian will. In case you're not keeping track: Nash Foster and my former student Mike Stay are running a company called, but they're working closely with RChain, run by Mike's friend Greg Meredith. Both these companies use a lot of math, like category theory. Christian and I are now being paid by Pyrofex to write papers; our first will be on enriched categories for operational semantics. Mike and Greg recently went on a European tour, talking a lot of top experts in category theory and computer science, offering them research grants to work with RChain. A bunch of these top experts are friends of mine, so this is pretty exciting. 3) I got contacted by Sam Stanton, who runs a research program on <a href = "https://www.arl.army.mil/www/default.cfm?page=206">Complex Dynamics and Systems</a> at the Army Research Office. He asked if I'd like to talk about funding and I said yes. This program seems right up my alley - here's the description: > The Complex Dynamics and Systems Program emphasizes fundamental understanding of the dynamics, both physical and information theoretic, of nonlinear and nonconservative systems as well as innovative scientific approaches for engineering and exploiting nonlinear and nonequilibrium physical and information theoretic dynamics for a broad range of future capabilities (e.g. novel energetic and entropic transduction, agile motion, and force generation). A common theme amongst all programmatic thrust areas is that systems of interest are "open" in the thermodynamic sense (or, similarly, dissipative dynamical systems). I haven't heard back from him yet; he was busy at a conference this week. But I'm optimistic.
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edited November 2018

5 April 2018:

1) Joe Moeller got invited to the Fields Institute to attend their program on Derived Geometry and Higher Categorical Structures in Geometry and Physics this summer, June 11 - 22! This is being run by my good friend Chenchang Zhu — a former student of Alan Weinstein who earlier had hired my student Chris Rogers for a postdoc at Goettingen, where she works.

Some really heavy-duty mathematicians are giving mini-courses: Chris Brav, Kevin Costello, Jacob Lurie, and Ezra Getzler. (No, not the Kevin Costello at UCR — the famous Kevin Costello.) As you all should know, Jacob Lurie is the guy who wrote the book on (infinity,1)-categories: the book called Higher Topos Theory. (I think Brendan has been attending Lurie's class on categorical logic.) So, this is great news!

2) About 250 people have registered for my course on applied category theory, and I'm writing a short "lecture" for them every day. You can see the notes here:

There are lots of good discussions, and I wish you actual students of mine would join in! Don't be so shy - this is your chance to get lots of cool people to know you!

3) Today I gave a talk on The Mathematics of Networks here at the math department at the University of Wisconsin, Madison. I'm talking to Gheorge Craciun and David Anderson about chemical reaction networks. I'm trying to set up a connection to symplectic geometry that generalizes the one Brendan, Blake and I found for electrical circuits and Markov processes. Namely: I think that for some class of chemical reaction networks, black-boxing should give a Lagrangian relation between input and output flows and concentrations. But since the equations are nonlinear, this will not be a linear relation.

The temperature is going down to 26 degrees Fahrenheit tonight — and 15 tomorrow night. Craciun told me the spring weather is nice and I'd see cherry blossoms, but he was apparently lying. I'll come back Sunday and try to thaw out.

Comment Source:5 April 2018: 1) Joe Moeller got invited to the Fields Institute to attend their program on <a href = "http://www.fields.utoronto.ca/activities/17-18/sms-2018">Derived Geometry and Higher Categorical Structures in Geometry and Physics</a> this summer, June 11 - 22! This is being run by my good friend Chenchang Zhu &mdash; a former student of Alan Weinstein who earlier had hired my student Chris Rogers for a postdoc at Goettingen, where she works. Some really heavy-duty mathematicians are giving mini-courses: Chris Brav, Kevin Costello, Jacob Lurie, and Ezra Getzler. (No, not the Kevin Costello at UCR &mdash; the <a href = "https://en.wikipedia.org/wiki/Kevin_Costello">famous</a> Kevin Costello.) As you all should know, Jacob Lurie is the guy who wrote the book on (infinity,1)-categories: the book called <i><a href = "https://arxiv.org/abs/math/0608040">Higher Topos Theory</a></i>. (I think Brendan has been attending Lurie's class on categorical logic.) So, this is great news! 2) About 250 people have registered for my course on applied category theory, and I'm writing a short "lecture" for them every day. You can see the notes here: <ul> <li> <a href = "http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory">Applied category theory</a>, <i>Azimuth Wiki</i>. </li> </ul> There are lots of good discussions, and I wish you actual students of mine would join in! Don't be so shy - this is your chance to get lots of cool people to know you! 3) Today I gave a talk on The Mathematics of Networks here at the math department at the University of Wisconsin, Madison. I'm talking to Gheorge Craciun and David Anderson about chemical reaction networks. I'm trying to set up a connection to symplectic geometry that generalizes the one Brendan, Blake and I found for electrical circuits and Markov processes. Namely: I think that for some class of chemical reaction networks, black-boxing should give a <i>Lagrangian</i> relation between input and output flows and concentrations. But since the equations are nonlinear, this will not be a linear relation. The temperature is going down to 26 degrees Fahrenheit tonight &mdash; and 15 tomorrow night. Craciun told me the spring weather is nice and I'd see cherry blossoms, but he was apparently lying. I'll come back Sunday and try to thaw out.
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edited November 2018

13 April 2018:

This week's progress:

1) Brandon Coya got a job interview at Whittier College! Cross your fingers and toes for Brandon.

2) Today Christian Williams is going to a Pyrofex developer's conference in Boulder, Colorado. After that he's gong to the RChain Spring Developer's Conference — for those of you not keeping score, Mike Stay's company Pyrofex is closely linked to Greg Meredith's company RChain, and both are interested in category theory. I'm hoping for a full report from Christian when he gets back - maybe even a blog article!

3) On Tuesday, Daniel Cicala gave a great talk in the network theory seminar on rewriting, going all the way from its origins in Chomsky's work on linguistics to graph rewriting, adhesive categories, and open objects in topoi! He covered a lot of ground in a very clear way.

• Jade Master, Open Petri nets and the reachability problem.

In computer science Petri nets are diagrams which are used to represent the transfer of resources in complex interacting systems of agents. These systems don’t usually exist in isolation and instead have inputs and outputs corresponding to external or environmental factors. To model this interconnectedness we define open Petri nets; Petri nets which can be glued together along specified inputs and outputs. We form a category of open Petri nets with open Petri nets as morphisms between their sets of inputs and outputs. Computer scientists are often interested in which states of a Petri net are reachable from a given initial state. We will put the category of open Petri nets to use by constructing reachability as a lax functor from the category of open Petri nets to the category of relations.

5) I got myself invited to Oxford to visit Jamie Vicary from June 22nd to August 20th. Jamie has long been in Abramsky and Coecke's research group in computer science at Oxford. He's still working there part-time, but he's gotten a permanent position at the University of Birmingham - 67 miles away, but easy by train. So, I will be talking to Jamie and others about category theory and computer science.

Comment Source:13 April 2018: This week's progress: 1) Brandon Coya got a job interview at Whittier College! Cross your fingers and toes for Brandon. 2) Today Christian Williams is going to a Pyrofex developer's conference in Boulder, Colorado. After that he's gong to the <a href = "https://developer.rchain.coop/rchain-developer-conference.pdf">RChain Spring Developer's Conference</a> &mdash; for those of you not keeping score, Mike Stay's company Pyrofex is closely linked to Greg Meredith's company RChain, and both are interested in category theory. I'm hoping for a full report from Christian when he gets back - maybe even a blog article! 3) On Tuesday, Daniel Cicala gave a great talk in the network theory seminar on rewriting, going all the way from its origins in Chomsky's work on linguistics to graph rewriting, adhesive categories, and open objects in topoi! He covered a lot of ground in a very clear way. 4) Today Jade Master is speaking in the graduate student seminar about open Petri nets: <ul> <li>Jade Master, Open Petri nets and the reachability problem. </li> </ul> > In computer science Petri nets are diagrams which are used to represent the transfer of resources in complex interacting systems of agents. These systems don’t usually exist in isolation and instead have inputs and outputs corresponding to external or environmental factors. To model this interconnectedness we define open Petri nets; Petri nets which can be glued together along specified inputs and outputs. We form a category of open Petri nets with open Petri nets as morphisms between their sets of inputs and outputs. Computer scientists are often interested in which states of a Petri net are reachable from a given initial state. We will put the category of open Petri nets to use by constructing reachability as a lax functor from the category of open Petri nets to the category of relations. 5) I got myself invited to Oxford to visit Jamie Vicary from June 22nd to August 20th. Jamie has long been in Abramsky and Coecke's research group in computer science at Oxford. He's still working there part-time, but he's gotten a permanent position at the University of Birmingham - 67 miles away, but easy by train. So, I will be talking to Jamie and others about category theory and computer science.
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edited November 2018

27 April 2018:

Here is some of this week's progress. A lot has been happening at the Applied Category Theory School, but I'll start with other things:

1) Blake Pollard got a 3-year National Research Council grant to continue his work at NIST and Carnegie Mellon! This is really great!

2) Daniel Cicala applied for and received a Dissertation Year Fellowship, which will support him for one quarter next year!

3) Joe Moeller put a paper on the arXiv:

Abstract. Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct a network model which can model networks with bounded degree. To do this, we generalize Green's graph products of groups to pointed categories which are finitely complete and cocomplete.

4) The Adjoint School part of Applied Category Theory 2018 is done! Four mentors - Aleks Kissinger, Pawel Sobocinski, Martha Lewis and myself - worked with teams of students to solve problems on causality, linear dynamical systems, linguistics and biology, respectively.

My team, from left to right here, consisted of Blake, Maru Saruzola doing algebraic K-theory at Cornell, Fabrizio Genovese working in Bob Coecke's quantum group in computer science at Oxford, and Jonathan Lorand doing symplectic geometry in a postdoc in Zurich:

We discovered some surprising results about the math of ATP coupling, and now we need to write them up. Meanwhile, Daniel and Joe were working with Pawel Sobocinski on circuits and signal flow diagrams, rediscovering some results that Brandon Coya and I have already written up, but maybe also some generalizations involving cartesian bicategories. Jade Master worked with Martha Lewis on translation using Lambek's pregroup grammars. Lots of great stuff!

Comment Source:27 April 2018: Here is some of this week's progress. A lot has been happening at the Applied Category Theory School, but I'll start with other things: 1) Blake Pollard got a 3-year National Research Council grant to continue his work at NIST and Carnegie Mellon! This is really great! 2) Daniel Cicala applied for and received a Dissertation Year Fellowship, which will support him for one quarter next year! 3) Joe Moeller put a paper on the arXiv: <ul> <li> Joe Moeller, <a href = "https://arxiv.org/abs/1804.07402">Noncommutative network models</a>. </li> </ul> > <b>Abstract</b>. Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct a network model which can model networks with bounded degree. To do this, we generalize Green's graph products of groups to pointed categories which are finitely complete and cocomplete. 4) The Adjoint School part of Applied Category Theory 2018 is done! Four mentors - Aleks Kissinger, Pawel Sobocinski, Martha Lewis and myself - worked with teams of students to solve problems on causality, linear dynamical systems, linguistics and biology, respectively. My team, from left to right here, consisted of Blake, Maru Saruzola doing algebraic K-theory at Cornell, Fabrizio Genovese working in Bob Coecke's quantum group in computer science at Oxford, and Jonathan Lorand doing symplectic geometry in a postdoc in Zurich: <img width = "500" src = "http://math.ucr.edu/home/baez/diary/leiden/students.jpg"> We discovered some surprising results about the math of ATP coupling, and now we need to write them up. Meanwhile, Daniel and Joe were working with Pawel Sobocinski on circuits and signal flow diagrams, rediscovering some results that Brandon Coya and I have already written up, but maybe also some generalizations involving cartesian bicategories. Jade Master worked with Martha Lewis on translation using Lambek's pregroup grammars. Lots of great stuff! 
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Thanks..interesting ..

Comment Source:Thanks..interesting ..
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7 May 2018:

Here's some of last week's progress. A lot of people said a lot of very interesting things at Applied Category Theory 2018, but I can't summarize all that. Here's just a bit.

1) I blogged about the paper that Brandon, Franciscus and I wrote:

2) On Friday I gave a talk about that paper. But I started by discussing the big picture: global warming, and what category theorists can do:

Abstract. The challenge of global warming brings into clear view the need for improved integration between category theory and other fields. Among other things, we need categories to understand networks. To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. All these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. Two complementary approaches are presentations of props using generators and relations (which are more algebraic in flavor) and decorated cospan categories (which are more geometrical). In this talk we focus on the former.

You can see the slides here and a video here.

3) Bob Coecke, Kathyrn Hess, Joshua Tan, Brendan, Nina and I launched a new journal on applications of category theory: Compositionality. I blogged about it here:

4) It's not really progress, but still some of you might be interested: I've decided I won't go to Oxford after all. The logistics were getting complicated, and I realized I'd be happier to stay here and write. So, I'll be around until August.

Right now it looks like I'll be going to Singapore from August 10th to September 17th.

Comment Source:7 May 2018: Here's some of last week's progress. A lot of people said a lot of very interesting things at Applied Category Theory 2018, but I can't summarize all that. Here's just a bit. 1) I blogged about the paper that Brandon, Franciscus and I wrote: * <a href = "https://johncarlosbaez.wordpress.com/2018/04/27/props-in-network-theory">Props in network theory</a>, <i>Azimuth</i>, 27 April 2018. 2) On Friday I gave a talk about that paper. But I started by discussing the big picture: global warming, and what category theorists can do: * <a href = "http://math.ucr.edu/home/baez/ACT2018/">Props in network theory</a>. <blockquote> <b>Abstract.</b> The challenge of global warming brings into clear view the need for improved integration between category theory and other fields. Among other things, we need categories to understand networks. To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. All these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. Two complementary approaches are presentations of props using generators and relations (which are more algebraic in flavor) and decorated cospan categories (which are more geometrical). In this talk we focus on the former. </blockquote> You can see the slides <a href = "http://math.ucr.edu/home/baez/ACT2018/act2018_web.pdf">here</a> and a video <a href = "http://math.ucr.edu/home/baez/ACT2018/act2018_web.pdf">here</a>. 3) Bob Coecke, Kathyrn Hess, Joshua Tan, Brendan, Nina and I launched a new journal on applications of category theory: Compositionality. I blogged about it here: * <a href = "https://johncarlosbaez.wordpress.com/2018/05/06/compositionality/">Compositionality</a>, <i>Azimuth</i>, 6 May 2018. 4) It's not really progress, but still some of you might be interested: I've decided I won't go to Oxford after all. The logistics were getting complicated, and I realized I'd be happier to stay here and write. So, I'll be around until August. Right now it looks like I'll be going to Singapore from August 10th to September 17th. 
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84.

11 May 2018:

This week's progress:

1) The really BIG news: Brandon Coya got a job! It's a 3-year visiting assistant professorship at Whittier College. I'm very happy about this.

He'll be teaching 4 courses a semester, which is a lot, but each semester lasts just 13 weeks. It's about an hour and fifteen minutes from UCR, so we may still be seeing him around. But first:

Brandon will be defending his thesis on Tuesday May 15th. Make sure to attend if you're in town!

2) I finished my online "lectures" on Chapter 1 of Brendan's book. If you don't know and love the proof of the adjoint functor for categories, which is rather technical, it's really nice to see the version for the special case of posets. Now I'm lecturing about resource theories, Petri nets, monoidal preorders and the like. One nice thing is that Tobias Fritz, an expert on resource theories, has joined the course and is helping out.

3) When I turn down tempting invitations I like to mention them here, so I don't feel quite as bad. Here's one:

Dear John,

We’re writing to ask for your help in reviewing proposals to FQXi for the grant program “Agency in the Physical World,” a program run in partnership with the Fetzer-Franklin Fund. Per FQXi’s process, we’ve invited proposals from about 45 PIs, which will be due June 11. We’re looking for help in

(a) reading and reviewing 13-15 proposals, and

(b) attending a 2.5-day in-person meeting to decide the grant awards.

The meeting will take place July 4-6 in Santa Cruz California (we apologize for the rather tight schedule as we had some delays in the first-round reviewing.)

The proposals will be of standard length (around 10 pages of core material), and we’d estimate 1.5 hours average time to review them. We also have a couple of things to sweeten the deal:

1) Along with of course covering the cost of the in-person meeting, we are able to offer an honorarium of $2000. 2) Immediately prior to the panel meeting (June 30-July 3) we will be having a small (~15-20 person) workshop on “The physics of the Observer,” bringing together a number of interesting people from the Bay Area, the Boston Area, and elsewhere, including the research groups of Max Tegmark and myself. We’d love to have you at this meeting (with expenses covered), though if you just want to serve on the panel that’s fine too. If you are able to attend and might want to, we can provide more detail to help you decide. (If you can’t do the panel but might want to attend the workshop, also let me know that.) What do you think? Best, Anthony Aguirre Comment Source:11 May 2018: This week's progress: 1) The really BIG news: Brandon Coya got a job! It's a 3-year visiting assistant professorship at Whittier College. I'm very happy about this. He'll be teaching 4 courses a semester, which is a lot, but each semester lasts just 13 weeks. It's about an hour and fifteen minutes from UCR, so we may still be seeing him around. But first: Brandon will be defending his thesis on Tuesday May 15th. Make sure to attend if you're in town! 2) I finished my online "lectures" on Chapter 1 of Brendan's book. If you don't know and love the proof of the adjoint functor for categories, which is rather technical, it's really nice to see the version for the special case of posets. Now I'm lecturing about resource theories, Petri nets, monoidal preorders and the like. One nice thing is that Tobias Fritz, an expert on resource theories, has joined the course and is helping out. 3) When I turn down tempting invitations I like to mention them here, so I don't feel quite as bad. Here's one: > Dear John, > We’re writing to ask for your help in reviewing proposals to FQXi for the grant program “Agency in the Physical World,” a program run in partnership with the Fetzer-Franklin Fund. Per FQXi’s process, we’ve invited proposals from about 45 PIs, which will be due June 11. We’re looking for help in > (a) reading and reviewing 13-15 proposals, and > (b) attending a 2.5-day in-person meeting to decide the grant awards. > The meeting will take place July 4-6 in Santa Cruz California (we apologize for the rather tight schedule as we had some delays in the first-round reviewing.) > The proposals will be of standard length (around 10 pages of core material), and we’d estimate 1.5 hours average time to review them. We also have a couple of things to sweeten the deal: > 1) Along with of course covering the cost of the in-person meeting, we are able to offer an honorarium of$2000. > 2) Immediately prior to the panel meeting (June 30-July 3) we will be having a small (~15-20 person) workshop on “The physics of the Observer,” bringing together a number of interesting people from the Bay Area, the Boston Area, and elsewhere, including the research groups of Max Tegmark and myself. We’d love to have you at this meeting (with expenses covered), though if you just want to serve on the panel that’s fine too. If you are able to attend and might want to, we can provide more detail to help you decide. (If you can’t do the panel but might want to attend the workshop, also let me know that.) > What do you think? > Best, > Anthony Aguirre
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85.
edited December 2018

19 May 2018:

This week's progress:

Brandon successfully defended his thesis! I just finished blogging about this thesis, which has a lot of great stuff in it. Here's the blog article, with a link to his actual thesis:

Brandon's thesis builds in a wonderful way on earlier work by Jason and Brendan, and it fits a lot of different diagrammatic languages for engineering into a nice framework:

I explain this diagram in my blog article!

Comment Source:19 May 2018: This week's progress: Brandon successfully defended his thesis! I just finished blogging about this thesis, which has a lot of great stuff in it. Here's the blog article, with a link to his actual thesis: * <a href = "https://johncarlosbaez.wordpress.com/2018/05/19/circuits-bond-graphs-and-signal-flow-diagrams/">Circuits, bond graphs, and signal-flow diagrams</a>, <i>Azimuth</i>, 19 May 2018. Brandon's thesis builds in a wonderful way on earlier work by Jason and Brendan, and it fits a lot of different diagrammatic languages for engineering into a nice framework: <img width = "600" src = "http://math.ucr.edu/home/baez/networks/coya_thesis/commutative_diagram_2.png"> I explain this diagram in my blog article!
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86.
edited December 2018

28 May 2018:

This week's progress:

1) Joe Moeller added a new idea to his paper on network models and submitted it for publication in Mathematical Structures in Computer Science. He chose Pawel Sobocinski as the editor to submit to.

He also put the new version on the arXiv:

Abstract. Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between all edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct the free network model on a given monoid, which can model networks with bounded degree. To do this, we generalize Green's graph products of groups to pointed categories which are finitely complete and cocomplete.

His new idea was that his construction of network models from monoids is really the left adjoint of the forgetful functor from network models to monoids! This makes it a lot more "conceptual".... and it should also be useful for designing networks.

2) Brandon Coya put his thesis on the arXiv:

3) In my online course I finished lecturing on Chapter 2 in Brendan and David's book. Check out some of these lectures:

We came up with some interesting thoughts on economics and category theory, which I'll need to develop later.

Comment Source:28 May 2018: This week's progress: 1) Joe Moeller added a new idea to his paper on network models and submitted it for publication in <i>Mathematical Structures in Computer Science</i>. He chose Pawel Sobocinski as the editor to submit to. He also put the new version on the arXiv: * Joe Moeller, <a href = "https://arxiv.org/abs/1804.07402">Noncommutative network models</a>. <blockquote><b>Abstract.</b> Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between all edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct the free network model on a given monoid, which can model networks with bounded degree. To do this, we generalize Green's graph products of groups to pointed categories which are finitely complete and cocomplete. </blockquote> His new idea was that his construction of network models from monoids is really the left adjoint of the forgetful functor from network models to monoids! This makes it a lot more "conceptual".... and it should also be useful for designing networks. 2) Brandon Coya put his thesis on the arXiv: * Brandon Coya, <a href = "https://arxiv.org/abs/1805.08290"><i>Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective</i></a>. 3) In my online course I finished lecturing on Chapter 2 in Brendan and David's book. Check out some of these lectures: * <a href = "https://johncarlosbaez.wordpress.com/2018/05/12/applied-category-theory-course-resource-theories/">Resource theories</a>, <i>Azimuth</i>, 12 May 2018. We came up with some interesting thoughts on economics and category theory, which I'll need to develop later.
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87.

1 June 2018:

This week's progress:

1) Adam Yassine is giving a talk on his work. And I may have forgotten to mention his May 14th talk in our network theory seminar!

• A category theoretic framework for analytical mechanics
Abstract. We initiate a program to formalize in a category theoretic framework the heuristic principles that physicists employ in constructing analytical mechanical models of classical physical systems. We work in the category of symplectic manifolds where morphisms are surjective Poisson maps. Decorated spans can be constructed in this category and the composition of isomorphism classes of decorated spans is defined using pullbacks. Certain Hamiltonian systems are mathematically described as compositions of isomorphism classes of decorated spans. The compositional elements correspond physically to the subsystems of the described system. A similar framework permits a category theoretic description of certain Lagrangian systems. A symmetric monoidal functor between the two categories translates between the Lagrangian and Hamiltonian perspectives.

2) My paper with Brandon, Props in network theory, was accepted for publication in Theory and Applications of Categories. This is the one where the referee thought we explained the symplectic geometry in too much detail, didn't understand the category theory, and passed it on to another referee. The second referee understood the category theory and liked the paper more!

We made the required changes, put the paper in TAC's format, and submitted it today. Now I can go back to fixing my paper with Brendan... which is another long story.

3) I got an email from Mario Rasetti, who heads ">ISI, that research center in Torino. He wrote:

I presented your proposal to our Science Board and they: i) confirmed their eager intention to proceed with the idea to create strong mathematics group, mostly focused on algebraic topology and category theory, in support of our research on topological data analysys; ii) checked with the Board of Directors of the Foundation that fresh sustainable funds for such operation are not available right now, but will be made available - if an interesting project is presented - for 2019: iii) agreed that you would be an excellent leader for this operation, provided you would agree to spend an adequate fraction of your time in Torino. At this point you and I should try and meet in person (perhaps in New York, at the site that ISI has there) to discuss how realistic all this is for you.
Comment Source:1 June 2018: This week's progress: 1) Adam Yassine is giving a talk on his work. And I may have forgotten to mention his May 14th talk in our network theory seminar! <ul> <li> A category theoretic framework for analytical mechanics </li> </ul> <blockquote> <b>Abstract.</b> We initiate a program to formalize in a category theoretic framework the heuristic principles that physicists employ in constructing analytical mechanical models of classical physical systems. We work in the category of symplectic manifolds where morphisms are surjective Poisson maps. Decorated spans can be constructed in this category and the composition of isomorphism classes of decorated spans is defined using pullbacks. Certain Hamiltonian systems are mathematically described as compositions of isomorphism classes of decorated spans. The compositional elements correspond physically to the subsystems of the described system. A similar framework permits a category theoretic description of certain Lagrangian systems. A symmetric monoidal functor between the two categories translates between the Lagrangian and Hamiltonian perspectives. </blockquote> 2) My paper with Brandon, <a href = "http://math.ucr.edu/home/baez/prop.pdf">Props in network theory</a>, was accepted for publication in <i>Theory and Applications of Categories</i>. This is the one where the referee thought we explained the symplectic geometry in too much detail, didn't understand the category theory, and passed it on to another referee. The second referee understood the category theory and liked the paper more! We made the required changes, put the paper in TAC's format, and submitted it today. Now I can go back to fixing my paper with Brendan... which is another long story. 3) I got an email from Mario Rasetti, who heads "><a href = "https://www.isi.it/en/home">ISI</a>, that research center in Torino. He wrote: <blockquote> I presented your proposal to our Science Board and they: i) confirmed their eager intention to proceed with the idea to create strong mathematics group, mostly focused on algebraic topology and category theory, in support of our research on topological data analysys; ii) checked with the Board of Directors of the Foundation that fresh sustainable funds for such operation are not available right now, but will be made available - if an interesting project is presented - for 2019: iii) agreed that you would be an excellent leader for this operation, provided you would agree to spend an adequate fraction of your time in Torino. At this point you and I should try and meet in person (perhaps in New York, at the site that ISI has there) to discuss how realistic all this is for you. </blockquote> 
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88.
edited February 2019

12 June 2018:

1) Today in our network theory seminar Joseph is talking about his latest paper:

Abstract. A network model is an algebraic formalism for modeling the construction of complex networks, in particular, communications networks. Previous constructions only produced relatively commutative network models. Certain types of networks demand a more expressive model. After reviewing the basic theory of network models, we construct the free network model on a given monoid. This construction utilizes various concepts, namely algebraic varieties, generalized graph products, and Kneser graphs. We will then realize graphs of bounded degree as an algebra of a noncommutative network model.

2) I forgot to mention this talk by Christian on May 4th in the grad student seminar! He also gave a related talk in our seminar, which I may also have forgotten to mention. Sorry!

• Categorical computation - form and content
Abstract. There is a duality of syntax and semantics – the form of a theory and the content of a model. This is a fundamental idea in category theory, which was introduced by William Lawvere in his 1963 PhD thesis. The notion of Lawvere theory provides an understanding of algebraic structures independent of presentation, improving upon the set-theoretic universal algebra. Soon after, these theories were proven equivalent to monads, the categorical manifestation of duality, through which the algebras of the monad correspond to models of the theory. Theories and monads provide complementary perspectives of algebraic structures, and both are becoming important to theoretical and practical computer science. We discuss the application to distributed computation, where enriched Lawvere theories can be used to create languages, programs, and data structures which have their operational semantics — the ways they can operate in context — integrated into their definition, effecting sound design of software.

3) I've been continuing my online course on applied category theory. Apart from this nothing much has been finished, as far as I can tell. I spent the last two weeks doing massive revisions on my paper with Brendan, "A compositional framework for passive linear circuits". Brendan spent the last couple weeks writing a draft of a paper with David Spivak, "Constructing hypergraph categories" - and this week he's gonna help me finish our paper. I'm starting to work with the ACT2018 students on a paper "Biochemical coupling through emergent conservation laws". Also, Greg Egan and I solved a fun puzzle:

If P: Set -> Set is the covariant power set functor, is there a way to define a natural transformation m: P^2 P^2 => P^2 that is associative?

It's well-known that P is a monad. It's recently been shown that P^2 cannot be made into a monad, but the proof of that didn't settle the above puzzle.

I got interested in the puzzle partially just because it's sort of mind-boggling: if the answer were "yes", we’d have a natural way to take a set of sets of sets of sets and turn it into a set of sets in such a way that the two most obvious resulting ways to turn a set of sets of sets of sets of sets of sets into a set of sets agree!

You can see the answer in the discussion here:

It turns out to be quite pretty. BUT, I want to keep finishing up papers!

Comment Source:12 June 2018: 1) Today in our network theory seminar Joseph is talking about his latest paper: <ul> <li> <a href = "https://arxiv.org/abs/1804.07402">Noncommutative network models</a> </li> </ul> <blockquote><b>Abstract.</b> A network model is an algebraic formalism for modeling the construction of complex networks, in particular, communications networks. Previous constructions only produced relatively commutative network models. Certain types of networks demand a more expressive model. After reviewing the basic theory of network models, we construct the free network model on a given monoid. This construction utilizes various concepts, namely algebraic varieties, generalized graph products, and Kneser graphs. We will then realize graphs of bounded degree as an algebra of a noncommutative network model.</blockquote> 2) I forgot to mention this talk by Christian on May 4th in the grad student seminar! He also gave a related talk in our seminar, which I may also have forgotten to mention. Sorry! <ul><li>Categorical computation - form and content</li></ul> <blockquote><b>Abstract.</b> There is a duality of syntax and semantics – the form of a theory and the content of a model. This is a fundamental idea in category theory, which was introduced by William Lawvere in his 1963 PhD thesis. The notion of Lawvere theory provides an understanding of algebraic structures independent of presentation, improving upon the set-theoretic universal algebra. Soon after, these theories were proven equivalent to monads, the categorical manifestation of duality, through which the algebras of the monad correspond to models of the theory. Theories and monads provide complementary perspectives of algebraic structures, and both are becoming important to theoretical and practical computer science. We discuss the application to distributed computation, where enriched Lawvere theories can be used to create languages, programs, and data structures which have their operational semantics &mdash; the ways they can operate in context &mdash; integrated into their definition, effecting sound design of software.</blockquote> 3) I've been continuing my <a href = "http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory+Course">online course on applied category theory</a>. Apart from this nothing much has been finished, as far as I can tell. I spent the last two weeks doing massive revisions on my paper with Brendan, "A compositional framework for passive linear circuits". Brendan spent the last couple weeks writing a draft of a paper with David Spivak, "Constructing hypergraph categories" - and this week he's gonna help me finish our paper. I'm starting to work with the ACT2018 students on a paper "Biochemical coupling through emergent conservation laws". Also, Greg Egan and I solved a fun puzzle: If P: Set -> Set is the covariant power set functor, is there a way to define a natural transformation m: P^2 P^2 => P^2 that is associative? It's well-known that P is a monad. It's recently been shown that P^2 cannot be made into a monad, but the proof of that didn't settle the above puzzle. I got interested in the puzzle partially just because it's sort of mind-boggling: if the answer were "yes", we’d have a natural way to take a set of sets of sets of sets and turn it into a set of sets in such a way that the two most obvious resulting ways to turn a set of sets of sets of sets of sets of sets into a set of sets agree! You can see the answer in the discussion here: <ul> <li> <a href = "https://golem.ph.utexas.edu/category/2018/06/sets_of_sets_of_sets_of_sets_o.html">Sets of sets of sets of sets of sets of sets</a></li></ul> It turns out to be quite pretty. BUT, I want to keep finishing up papers!
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89.
edited February 2019

22 June 2018:

1) Brendan Fong wrote:

Just this minute, David Spivak and I had a paper appear on the arXiv! It's called Hypergraph categories, and is about hypergraph categories. Maru and I are also working on something about Kan extensions and decorated corelations (but I'm not sure it's good forum material). I'm also lagging behind on helping John finish up the circuits paper. Tomorrow I leave for Toposes in Como. Then I'll be at the 2nd Workshop on Open Games, in Oxford, and then at CT 2018. Perhaps I'll see some of you somewhere!

2) Nina Otter wrote:

Yesterday I received my Leave to Supplicate, which means that I have officially finished my PhD. Yay! Also just in time, as on Sunday I am flying to Los Angeles where I'll be for two weeks for the paperwork for my UCLA appointment.

3) Daniel Cicala wrote:

My HoTT collaborators and I made a bit of a breakthrough on this thing we've been trying to prove for awhile now. It's technical detail stuff, so not too interesting, but has been bugging us forever it seems. Also, I've been chatting with potential mentors about ACT2019. There's some excitement out there.
Comment Source:22 June 2018: 1) Brendan Fong wrote: <blockquote> Just this minute, David Spivak and I had a paper appear on the arXiv! It's called <a href = "https://arxiv.org/abs/1806.08304">Hypergraph categories</a>, and is about hypergraph categories. Maru and I are also working on something about Kan extensions and decorated corelations (but I'm not sure it's good forum material). I'm also lagging behind on helping John finish up the circuits paper. Tomorrow I leave for <a href = "http://tcsc.lakecomoschool.org/">Toposes in Como</a>. Then I'll be at the <a href = "https://julesh.com/second-workshop-on-open-games/">2nd Workshop on Open Games</a>, in Oxford, and then at <a href = "http://www.mat.uc.pt/~ct2018/">CT 2018</a>. Perhaps I'll see some of you somewhere! </blockquote> 2) Nina Otter wrote: <blockquote> Yesterday I received my Leave to Supplicate, which means that I have officially finished my PhD. Yay! Also just in time, as on Sunday I am flying to Los Angeles where I'll be for two weeks for the paperwork for my UCLA appointment. </blockquote> 3) Daniel Cicala wrote: <blockquote> My HoTT collaborators and I made a bit of a breakthrough on this thing we've been trying to prove for awhile now. It's technical detail stuff, so not too interesting, but has been bugging us forever it seems. Also, I've been chatting with potential mentors about ACT2019. There's some excitement out there. </blockquote>
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90.

30 June 2018:

Congratulations, Nina, for getting your PhD! Welcome to Los Angeles!

Congratulations, Brendan, for putting Hypergraph categories on the arXiv with David! Hypergraph categories are very important for network theory — categories of decorated cospans and corelations are key examples — so all my students should read this paper.

Congratulations, Daniel, for making progress on that HoTT paper!

More progress:

1) Daniel has prepared an NSF proposal to get money for students to attend ACT2019 in Oxford. This is just the first step of actually submitting the proposal.

Daniel also has lots of other ACT2019-related tasks left on his plate - some of them fun, like contacting potential mentors. But with luck all this will succeed and Daniel will learn a lot and get to know some people who will eventually want to hire him.

2) A bunch of us put a paper on the arXiv based on our work at ACT2018:

It explains all the chemistry and biology prerequisites, so don't be scared! You'll be much cooler after you read it. But I suggest this version on my blog, which is a bit more chatty and lets people ask questions:

Comment Source:30 June 2018: Congratulations, Nina, for getting your PhD! Welcome to Los Angeles! Congratulations, Brendan, for putting Hypergraph categories on the arXiv with David! Hypergraph categories are very important for network theory &mdash; categories of decorated cospans and corelations are key examples &mdash; so all my students should read this paper. Congratulations, Daniel, for making progress on that HoTT paper! More progress: 1) Daniel has prepared an NSF proposal to get money for students to attend ACT2019 in Oxford. This is just the first step of actually submitting the proposal. Daniel also has lots of other ACT2019-related tasks left on his plate - some of them fun, like contacting potential mentors. But with luck all this will succeed and Daniel will learn a lot and get to know some people who will eventually want to hire him. 2) A bunch of us put a paper on the arXiv based on our work at ACT2018: <ul> <li> John Baez, Jonathan Lorand, Blake Pollard and Maru Sarazola, <a href = "https://arxiv.org/abs/1806.10764">Biochemical coupling through emergent conservation laws</a>. </li> </ul> It explains all the chemistry and biology prerequisites, so don't be scared! You'll be much cooler after you read it. But I suggest this version on my blog, which is a bit more chatty and lets people ask questions: <ul> <li><a href ="https://johncarlosbaez.wordpress.com/2018/06/27/coupling-through-emergent-conservation-laws-part-1/">Coupling through emergent conservation laws</a>. </li> </ul>