Monads, like burritos, come in many different varieties. In computer science monads serve to streamline computational patterns such as exception handling and context management. We illustrate these ...

Whenever someone says “quick question”, I’m unable to give them a quick answer. Is that the case here?

Mar 26, 2025 The McGee group is one of the two smallest groups with an outer automorphism that preserves conjugacy classes. My route to understanding this fact was a long and winding one.

This seems to represent quite a small proportion of all finite groups, counted by order, even ignoring the p p-groups. And this phenomenon of needing roots of unity to define representations is not ...

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, ...

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, ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

I keep wanting to understand Bernoulli numbers more deeply, and people keep telling me stuff that’s fancy when I want to understand things simply. But let me try again.

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 ...

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: ...

Here is the statement as I understand it to be, framed as a bijection of sets. My chief reference is the wonderful book Elliptic Curves, Modular Forms and their L-Functions by Álvaro Lozano-Robledo ...