Today I heard from David Benson that Jack Morava died yesterday. This comes as such a huge shock that I can’t help but hope Benson was somehow misinformed. Morava has been posting comments to the ...

August 2025's Entries Jack Morava Random Past Entries TeXnical Issues Sage advice on viewing this blog and posting comments thereon. Optimal Transport and Enriched Categories IV: Examples of Kan-type ...

Quick question. Classically the harmonic oscillator Hamiltonian is often written 1 2 ( p 2 + q 2), while quantum mechanically it gets some extra ‘ground state energy’ making the Hamiltonian ...

Did you know that Lawvere did classified work on arms control in the 1960s, back when he was writing his thesis? You can read more here: Yes, that’s right. For technical reasons the n-Category Café ...

• a 2-rig over a field k is a Cauchy complete k -linear symmetric monoidal category is a line object if there’s an object y with x ⊗ y ≅ I. is a bosonic line object if it is a line object and the ...

How do you count rooted planar n -ary trees with some number of leaves? For n = 2 this puzzle leads to the Catalan numbers. These are so fascinating that the combinatorist Richard Stanley wrote a ...

Last time I began explaining how a chunk of combinatorics is categorified ring theory. Every structure you can put on finite sets is a species, and the category of species is the free symmetric 2-rig ...

These are some lecture notes for a 4 1 2 -hour minicourse I’m teaching at the Summer School on Algebra at the Zografou campus of the National Technical University of Athens. To save time, I am ...

We’re brought up to say that the dual concept of injection is surjection, and of course there’s a perfectly good reason for this. The monics in the category of sets are the injections, the epics are ...

Namely, I want to prove a wonderful known fact about random permutations, the Cycle Length Lemma, using a bit of category theory. The idea here is that the number of k k -cycles in a random ...

September 2024's Entries The Space of Physical Frameworks (Part 5) Let’s think about how classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant \ (k\) ...