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 ...

Oct 10, 2024 John Baez, Joe Moeller and Todd Trimble have a new paper out that rethinks the splitting principle in the context of categorified rigs, or ‘2-rigs’.

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 ...

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, ...

Oct 10, 2024 John Baez, Joe Moeller and Todd Trimble have a new paper out that rethinks the splitting principle in the context of categorified rigs, or ‘2-rigs’.

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.

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 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 ...

Sep 30, 2024 Let’s think about how classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant \(k\) approaches zero, by looking at an example.

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 ...