In the last episode of my column in Notices of the American Mathematical Society, we looked at a particle moving in an attractive central force whose strength is proportional to the inverse cube of ...

This week, 50 category theorists and software engineers working on “safeguarded AI” are meeting in Bristol. They’re being funded by £59 million from ARIA, the UK’s Advanced Research and Invention ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

In the beginning, there were hardly any spaces whose magnitude we knew. Line segments were about the best we could do. Then Mark Meckes introduced the technique of potential functions for calculating ...

Applied category theorists are flocking to AI, because that’s where the money is. I avoid working on it, both because I have an instinctive dislike of ‘hot topics’, and because at present AI is mainly ...

I want to go back over something from Part 11, but in a more systematic and self-contained way. I’m stating these facts roughly now, to not get bogged down. But I’ll state them precisely, prove them, ...

Previously: Part 5. Next: Part 7. A category theorist might imagine that a chapter with this title would be about constructing colimits, and they’d be half right.

I’ve just arXived my notes for Edinburgh’s undergraduate Galois theory course, which I taught from 2021 to 2023. I first shared the notes on my website some time ago. But it took me a while to arXiv ...

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 ...

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 ...

Fibrations are a fundamental concept of category theory and categorical logic that have become increasingly relevant to the world of applied category theory thanks to their prominent use in ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...