The Octoberfest is a noble tradition in category theory: a low-key, friendly conference for researchers to share their work and thoughts. This year it’s on Saturday October 26th and Sunday October ...

I called this chapter of my course “Relations”, but I should have called it “Specifying subsets and functions”, because that’s what it’s all about. This week, we saw that it’s possible to define ...

I haven’t been carefully following quantum field theory these days, but some folks on the Category Theory Community Server asked me what I thought about recent work using the ‘amplitudohedron’ and ...

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, ...

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 ...

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 ...

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.

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.