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 ...

The Kan Extension Seminar II continues with a discussion of the paper Notions of Lawvere Theory by Stephen Lack and Jirí Rosický. To read more about classical Lawvere theories, you can read Evangelia ...

My friend the combinatorist Bill Schmitt breezed through Paris recently, taking a train back from Hopf-in-Lux with Paul-André Melliès, and spending a day here before going home to DC. We had some time ...

Where did we get to in our discussion of the two cultures of mathematics? To explore the possibility that interaction may be possible between what Gowers called ‘combinatorics’ and our Café subculture ...

Now that I finally understand the proof of the Wedderburn–Artin Theorem, I want to do what any good category theorist would do: formulate it more generally and abstractly, so nobody can understand me ...

I’ve just arXived a new paper: The categorical origins of Lebesgue integration (arXiv:2011.00412). Longtime Café readers may remember that I blogged about this stuff back in 2014, but I’ve only just ...

In this week’s lecture on Quantization and Cohomology, we’ll start digging deeper into what quantization is really about: Week 11 (Jan. 23) - Action as a functor from a category of “configurations” ...

Michael Barr has spent a lot of time and effort translating Grothendieck’s legendary “Tohoku” paper into English. If you don’t mind violating Grothendieck’s stated wishes, you can now read this ...

A Yoneda structure on a 2-category consists of two pieces of data satisfying three axioms. We will see that the data is what is necessary to naturally express the Yoneda lemma in the 2-category, and ...

Furthering my study of coalgebra, I came across slides for a couple of talks (here and here) which put John and Jim’s microcosm principle into a coalgebraic context. Recall their claim in ...

There’s been a bunch of discussion online recently (e.g. SBS, MathOverflow 1, 2, 3, etc.) about set-theoretic foundations for category theory, the role of universes, and so on. So I thought I would ...

I will give an overview of the results and methods used in this paper. Also, especially towards the end of my post, I will also indicate some points that I think could still be clarified further by ...