Combinatorics, or at least part of it, is the art of counting. For example: how many derangements does a set with n n elements have? A derangement is a bijection with no fixed points. We’ll count them ...

You can classify representations of simple Lie groups using Dynkin diagrams, but you can also classify representations of ‘classical’ Lie groups using Young diagrams. Hermann Weyl wrote a whole book ...

I want to go back over something from Part 11, but in a more systematic and self-contained way. I’m stating these facts roughly now, to not get bogged down. But I’ll state them precisely, prove them, ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...

String diagrams are ubiquitous in applied category theory. They originate as a graphical notation for representing terms in monoidal categories and since their origins, they have been used not just as ...

This is part two of a three part series of expository posts on our paper Displayed Type Theory and Semi-Simplicial Types. In this part, we cover the main results of the paper.

I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to learn, only to have my ...

This is part one of a three-part series of expository posts on our paper Displayed Type Theory and Semi-Simplicial Types. In this part, we motivate the problem of constructing SSTs and recap its ...

James Dolan and Chris Grossack and I had a fun conversation on Monday. We came up some ideas loosely connected to things Chris and Todd Trimble have been working on… but also connected to the ...

These are notes for the talk I’m giving at the Edinburgh Category Theory Seminar this Wednesday, based on work with Joe Moeller and Todd Trimble. (No, the talk will not be recorded.) They still have ...