This phase of the course is all about building up the basic apparatus. We’ve stated our axioms, and it might seem like they’re not very powerful. It’s our job now to show that, in fact, they’re ...

Then form the free k -linear symmetric monoidal category on S by freely forming k -linear combinations of morphisms. This is called kS. Up to equivalence, it has one object for each natural number n, ...

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 ...

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 ...

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

Sep 3, 2020 Announcing the Johns Hopkins category theory seminar, which will be held online during the second half of 2020.

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 ...

We’ve just finished the second week of my undergraduate Axiomatic Set Theory course, in which we’re doing Lawvere’s Elementary Theory of the Category of Sets but without mentioning categories. This ...

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.

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 ...