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 ...

“Solid ring” sounds self-contradictory, since a ring should have a hole in it. But mathematicians use words in funny ways. Here’s one reason this is interesting: the category of affine schemes is the ...

This is a monoidal bicategory, since we can take the tensor product of algebras, and everything else gets along nicely with that. But Jacob Lurie said the Postnikov invariants are trivial in this case ...

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 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 ...

I’ve been blogging a bit about medieval math, physics and astronomy over on Azimuth. I’ve been writing about medieval attempts to improve Aristotle’s theory that velocity is proportional to force, ...

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 algebraic K K-groups of the integers, and other rings, are a big deal. A lot of fairly recent progress on understanding them is due to Voevodsky, Rost, Rognes and Weibel, whose work culminated in ...

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 ...