any generation of Standard Model fermions transforms as the direct sum of six irreducible representations: These correspond to the six types of left-handed fermion: q L, d R, u R, ℓ L, e R, ν R. Six ...

Jul 18, 2026 John Baez, Endre Bokor and Latham Boyle have a new paper called “Jordan pair quantum theory and the Standard Model”.

Bless British trains. A two-hour delay with nothing to occupy me provided the perfect opportunity to figure out the relationships between some of the results that John, Tobias and I have come up with ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

Over the last few years, I’ve been very slowly working up a short expository paper — requiring no knowledge of categories — on set theory done categorically. It’s now progressed to the stage where I’d ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

Last time I reviewed a bit of Bott periodicity. Now I want to start leading up to a question about it. It will take a while. So, this time, I will explain a wonderful one-to-one correspondence between ...

String diagrams are ubiquitous in applied category theory. They originate as a graphical notation for representing terms in monoidal categories and since their origins, they have been used not just as ...

This blog post discusses the paper “Compositional Thermostatics” by John Baez, Owen Lynch, and Joe Moeller. The series of posts on Dr. Baez’s blog gives a more thorough overview of the topics in the ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

We start by introducing Petri nets and elementary Petri nets, which will be the focus of this post. In general, the weight of each condition can be an integer. In the case of elementary Petri nets, ...

Freeman Dyson is a famous physicist who has also dabbled in number theory quite productively. If some random dude said the Riemann Hypothesis was connected to quasicrystals, I’d probably dismiss him ...