Here’s some basic information about the next big annual applied category theory conference — Applied Category Theory 2025 — and the school that goes along with that: the Adjoint School. James ...

A function is determined by its effect on elements. That is, define an element of a set S S as a function 1 → S \mathbf {1} \to S. Then whenever f, g: X → Y f, g:X \to Y with fx = gx f x = g x for all ...

7. For every function f: X → Y f: X \to Y and element y ∈ Y y \in Y, we can form the fibre f − 1 (y) f^{-1}(y). Category theorists will recognize this as a special case of the existence of pullbacks.

In Part 4, I presented a nifty result supporting my claim that classical statistical mechanics reduces to thermodynamics when Boltzmann’s constant k k approaches zero. I used a lot of physics jargon ...

Hopefully, you didn’t notice, but Golem V has been replaced. Superficially, the new machine looks pretty much like the old. It’s another Mac Mini, with an (8-core) Apple Silicon M2 chip (instead of a ...

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 ...

Why do I care? As we’ll see later, classical statistical mechanics features a crucial formula that involves a Laplace transform. So it would be great if we could find some parameter β \beta in that ...

I’m teaching Edinburgh’s undergraduate Axiomatic Set Theory course, and the axioms we’re using are Lawvere’s Elementary Theory of the Category of Sets — with the twist that everything’s going to be ...