If you don't want to talk about the permutation group actions, just talk about "planar" or "nonpermutative" operads, which are probably more often called "multicategories". They're what you get when you leave out everything about these permutation …
Hi -
Some comments:
1) In your initial definition you don't say the identity morphism is called $\mathrm{Id}_A : A \to A$. This is presumably a deliberate trick to make things easier to read. If so, fine.
2) You also don't include a notation fo…
The forum is not very active now, but you can still get a lot out of it by starting the course here:
[[Applied Category Theory Course]].
You'll see 77 "lectures" on Fong and Spivak's book (which is free online), and lots of solved exercises, and…
Hi! I bet there's a lot of great applications of category theory to linear programming or convex programming. They're the sort of mathematical subject that lends itself to category theory. Unfortunately I don't know exactly what to try first.
Th…
Hi! The forum is not very active now, but you can still get a lot out of it by starting the course here:
[[Applied Category Theory Course]].
You'll see 77 "lectures" on Fong and Spivak's book (which is free online), and lots of solved exercises…
Another talk:
February 19, 2019: Kenny Courser
Category theory for genetics
Abstract. Rémy Tuyéras has developed a categorical framework aimed at handling various commonly studied subjects from the theory of genetics. Some of these include…
We received 125 applications for the ACT2019 Adjoint School and Daniel Cicala and Jules Hedges have chosen about 20 students from among these, who will be receiving notifications soon. It's a great team of people, and I look forward to seeing them…
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…
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 d…
12 June 2018:
1) Today in our network theory seminar Joseph is talking about his latest paper:
Noncommutative network models
Abstract. A network model is an algebraic formalism for modeling the construction of complex networks, in particular…
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 in…
Julio - I meant for \(X\) and \(Y\) to be countries, \(x \in X\) to be a city in the country \(X\), and \(y \in Y\) to be a city in the country \(Y\).
So, just one word in my description was wrong, and I'll fix it now. Thanks for catching it!
And…
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.…