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 pu…
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:
Circuits, bond graphs, …
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…
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 …
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 …
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'…
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 …
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! D…
20 March 2018:
This week's progress:
1) Brendan came out with a new book:
Brendan Fong and David I. Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory.
Abstract. This book is an invitation to discover adv…
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, Cognition, convexity and category theory.
I love the category of …
3 March 2018:
1) I posted another blog article written by students at the ACT2018 school:
Jonathan Lorand and Fabrizio Genovese, Hypergraph categories of cospans, The n-Category Café, February 28, 2018.
This is a nice introduction to …
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 23-2…
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 fo…
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 w…
1 February 2018:
1) Today this paper by Daniel Cicala was published in TAC!
Daniel Cicala, Spans of cospans.
Abstract. We study spans of cospans in a category C and explain how to horizontally and vertically compose these. When C is a topos …
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.…
Hi, folks! I'm teaching a course on category theory at UCR, and there are some hand-written notes here:
Category theory course.
I'm not sure it's possible to follow the course from these notes; there's a lot that I say out loud, and even some …
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…
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 …
Jesus: if you want more on (slightly) higher categories, try these papers by students of mine. That's what we're mainly working on these days! I have carefully edited all these papers:
Kenny Courser, A bicategory
of decorated cospans, Theory and…
Yes, Peter, the course is over. I don't think "temporarily" is a good adverb to insert here. Sorry!
However, the book by Fong and Spivak is still there for you to read, along with Tai-Danae Bradley's excellent short book. I also have zillions of…
Thanks, folks!
I am now teaching an advanced course in category theory at UCR; I'm trying to get someone to take really good readable notes and make those public, but it hasn't happened quite yet.
I will definitely keep updating "This Week's Progr…
Keith - a \(\mathbf{Bool}\)-profunctor \(\Phi \colon \mathcal{X} \to \mathcal{X}\) is a kind of relation from a preorder \(\mathcal{X}\) to itself, namely a feasibility relation. But we can look at the set of elements of \(\mathcal{X}\) that are r…
Christopher wrote:
Okay, one thing I keep noticing is that in these "richer" "spaces" (especially in CS applications) its often much more natural to define division then subtraction.
Yes, this is why people invented fractions long before they …
Thanks, folks! I may add Daniel's "No Pain, No Gain" threads, and others, up to the "officially announced" section of the discussions to make them easier to find.
There's a lot more pain, and gain, available from the readings I just listed. Tai-…
Igor wrote:
How do \(k\)-valued matrices act on finite sets?
They don't, nor need they. In general, morphisms don't act on objects. You just need to know what a morphism from one object to another is, and how to compose them.
To a modern …
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 pa…
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, …