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 ...

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

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 ...

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, ...

Faster-than-light neutrinos? Boring… let’s see something really revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called Elements in which he claims to prove the ...

Bless British trains. A two-hour delay with nothing to occupy me provided the perfect opportunity to figure out the relationships between some of the results that John, Tobias and I have come up with ...

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 ...

I have been looking for examples, accessible to a lay audience, to illustrate the prevalence of cohomology. Here are some possibilities: ...

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 ...

Peter Aczel was the initial advocate of such a thing here, and I think it’s a great idea. Given that computer proof assistants are not really yet sufficiently automated to make formalization of ...

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 ...

Category theory has an excellent track record of formalizing intuitive statements of the form “this is the canonical such and such”. It has been especially effective in topology and algebra. But what ...