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”.

Jul 8, 2026 13:57 So you are disagreeing with Paul: you’re getting S(U(3)×U(2))\text{S}(\text{U}(3) \times \text{U}(2)) where he is getting SU(3)×SU(2)\text{SU}(3 ...

In order to get used to the calculus of exact squares, the first thing we have to change is to start thinking more in terms of Kan extensions rather than limits and colimits. For instance, it’s usual ...

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 ...

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 ...

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, ...

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, ...

The study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...