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

Jun 1, 2025 Todd Trimble and I wrote a paper on characterizing classical groups (and monoids) in terms of their 2-rigs of representations.

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a ...

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, ...

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 ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...

You probably know that the 2010 Fields Medals have been announced. The thing is, I’ve never succeeded in understanding the slightest thing about it. It’s as if it’s got a hard, shiny shell—it resists ...

The study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...

Over the last few years, I’ve been very slowly working up a short expository paper — requiring no knowledge of categories — on set theory done categorically. It’s now progressed to the stage where I’d ...

This is the first of a series of posts on how large cardinals look in categorical set theory. My primary interest is not actually in large cardinals themselves. What I’m really interested in is ...

We start by introducing Petri nets and elementary Petri nets, which will be the focus of this post. In general, the weight of each condition can be an integer. In the case of elementary Petri nets, ...