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 ...

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’.

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 ...

Hello unknown@52.167.144.231. So nice of you to stop by. I'm a member of the Theory Group here at UT. I've been at UT since September 1994. Before coming here, I was an Assistant Professor in the ...

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 ...

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 ...

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.

Sep 28, 2024 17:34 Not for now. I might share them after the course is over (early December). There’s a lot for me to ...