Feb 5, 2009 Notes from a talk by Ieke Moerdijk on dendroidal sets, with a few remarks on presheaves on the category of posets. 101 things to do with a 2-classifier Jan 17, 2008 What to do with a ...

May 24, 2017 Summarizes a new paper “A type theory for synthetic $\infty$-categories” by Emily Riehl and Mike Shulman. Jul 29, 2013 Let’s take a look at the E 8 lattice and the Lie algebra by the same ...

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 ...

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 ...

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 ...

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 ...

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 ...

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.

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, ...

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 ...

Last time I started talking about the groupoid of ‘finite sets equipped with permutation’, Perm \mathsf{Perm}. Remember: Today I’d like to talk about another slightly bigger groupoid. It’s very pretty ...