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 ...

Arkani-Hamed has the amusing, informal yet clear manner of someone like Feynman or Coleman. And he explains, step by step, how imaginary particle physicists in some other universe could have invented ...

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’.

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 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 ...

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 ...