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 ...

Jun 29, 2015 A new preprint explains Reedy categories from a category-theoretic point of view, as certain iterated collages of profunctor diagrams.

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 ...

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 ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

The plan for this series is to talk about ever larger sets and ever stronger axioms. So far we’ve looked at weak limits, strong limits, and alephs. Today we’ll look at beths. The beths are the sets ...

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 ...

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 ...

I have three questions. I have some guesses about the answers, so don’t think I’m completely clueless. But I’m clueless enough that I’d prefer to just give the questions, not my guesses.

Last summer my students Brendan Fong and Blake Pollard visited me at the Centre for Quantum Technologies, and we figured out how to understand open continuous-time Markov chains! I think this is a ...

an appreciation of Bill Lawvere’s work in this direction. More is behind the above link. The idea behind the term is that a geometric space is roughly something consisting of points or pieces that are ...