March 2026 Archives | The n-Category Café

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March 2026
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March 2026's Entries

A Typed Language for Agent Coordination
- Mar 11, 2026
- A category-theoretic approach to “agent frameworks”: that is, frameworks for coordinating “agents” that are large language models.

Random Past Entries

TeXnical Issues
- September 2, 2006
- Sage advice on viewing this blog and posting comments thereon.
Lectures on Classical Mechanics
- Dec 21, 2006
- Lectures notes on classical mechanics - now available in printed form!
Coenergy
- Jan 4, 2010
- What’s coenergy? Is ‘kinetic coenergy’ just kinetic energy regarded as a function of velocity rather than momentum?
A Topos for Algebraic Quantum Theory
- Dec 6, 2007
- A summary of some key points of Chris Heunen’s and Bas Spitters’ article.
Democracy and Mathematics
- Oct 4, 2010
- A message from André Joyal on reforming mathematics.
Chasing around the Triangle
- Aug 17, 2009
- Steve Awodey compares foundational frameworks: sets, types and categories.

Recent Comments

The Univalence Principle (4)
- Kevin MacDonald
  - Feb 21, 2026 01:34
  - OT: OT as only result for any of my posts due to relative mathematical ignorance. I just wanted to say ...
- Dimitris
  - Feb 13, 2026 18:05
  - Correct, “recently published” should be read more as “recently (with respect to preprint completion) published”…
- Mike Shulman
  - Feb 12, 2026 20:08
  - I think you answered your own question. Four years from preprint to publication is a bit long, but it (and ...
- RodMcGuire
  - Feb 12, 2026 19:59
  - Why is this published today in 2026 when the book it links to is a 2022 arXiv submission? well, AMS ...

Dynamics in Jordan Algebras (9)
- John Baez
  - Feb 17, 2026 05:35
  - Thanks, Blake! Fixed!
- Blake Stacey
  - Feb 17, 2026 03:46
  - The second-to-last line should end with an XX, not an AA.
- John Baez
  - Nov 24, 2025 12:20
  - Great, thanks! That’s good to know.
- Ed
  - Nov 24, 2025 08:15
  - I had a closer look at Braun and Koecher. The result you want is Satz 3.1 on page 281. The ...
- John Baez
  - Nov 10, 2025 14:06
  - Thanks! I’m now quite interested in whether all derivations of finite-dimensional Jordan algebras are inner. Your idea of complexifying the ...

Weil, Venting (16)
- David Roberts
  - Feb 2, 2026 11:33
  - Working link: https://doi.org/10.1007/s10516-022-09628-0
- L. B.
  - Jan 28, 2026 16:01
  - Despite being more than ten years late to the discussion, I think it might be of interest to you, with ...
- Graham White
  - Nov 16, 2015 12:10
  - It’s certainly true that there is too much excommunication, and denigration of other styles, in mathematics (this is trivially true, ...
- Gejza Jenča
  - Nov 13, 2015 07:42
  - Yes. No.
- Blake Stacey
  - Nov 13, 2015 00:52
  - The various translations I find online of Zhuangzi’s parable of the Dexterous Butcher have an extra line at the end, ...

Axioms for the Category of Hilbert Spaces (bis) (16)
- Blake Stacey
  - Jan 29, 2026 10:19
  - I’ve been trying to pull together various different approaches to reconstructing quantum theory from physical principles, which has brought me ...
- John Baez
  - Jan 12, 2022 23:42
  - Dusk. The alley is secreted in mist. The miserly reflection of the single lamp on the cobblestones makes you nervous. ...
- Chris Heunen
  - Nov 4, 2021 10:31
  - Thanks Jamie! The first version of the arxiv preprint was very lean and to the point. We’ve now updated it ...
- Jamie Vicary
  - Oct 1, 2021 12:30
  - Chris and Andre, it’s so nice to see this amazing result, congratulations! What surprises me most about it is the ...
- L Spice
  - Sep 30, 2021 04:17
  - But it’s unsatisfactory to characterise a small thing by really characteristing a big thing and saying how the small thing ...

Coxeter and Dynkin Diagrams (6)
- Layra
  - Jan 23, 2026 00:44
  - Perhaps a different way of looking at SU(2)SU(2) and ℤ 2\mathbb{Z}_2 is as the automorphism groups of ℍ\mathbb{H} and ℂ\mathbb{C} ...
- John Baez
  - Jan 22, 2026 05:42
  - That’s an interesting puzzle. I don’t have anything great to say about it. It reminds me of how people work ...
- Allen Knutson
  - Jan 22, 2026 03:36
  - Here’s something that’s always bugged me about Dynkin diagrams. On the one hand, you can use the Serre presentation of ...
- John Baez
  - Jan 15, 2026 23:56
  - Yes. Yes.
- Jeffery Winkler
  - Jan 13, 2026 19:22
  - Do you talk about their connection with the Platonic solids and other regular polytopes? Do you talk about how they ...

Octonions and the Standard Model (Part 13) (4)
- John Baez
  - Jan 20, 2026 21:57
  - Yes! We only get the beautiful description of one generation of fermions as the exterior algebra Λℂ 5\Lambda \mathbb{C}^5 if ...
- Jeffery Winkler
  - Jan 20, 2026 18:41
  - Does this include right-handed neutrinos?
- John Baez
  - Dec 19, 2025 10:12
  - It should be ℂ,ℝ\mathbb{C}, \mathbb{R} and ℍ\mathbb{H}, since typical complex representations are not self-dual. Thanks for noticing that something was ...
- David
  - Dec 19, 2025 10:00
  - Hi, John, Should this “division algebras ℂ,ℂ and ℍ, respectively” be ” division algebras ℝ, ℂ and ℍ, respectively”. David

Questions About the Néron–Severi Group (8)
- John Baez
  - Jan 19, 2026 17:13
  - I apologize for the incredibly late thanks, but thanks — I’m reviewing this material now, and your comment is again ...
- Jorge Vitório Pereira
  - Aug 2, 2022 14:41
  - [BL]=Complex Abelian Varieties by Birkenhake and Lange. The Néron-Severi group can be identified with the intersection of H 1,1(X)H^{1,1}(X) and ...
- John Baez
  - Feb 18, 2022 20:54
  - I saw someone say that somewhere, but I didn’t trust them. This would completely change my mental picture, so if ...
- John Baez
  - Feb 17, 2022 20:40
  - Thanks, Tim! I’ll check it out.
- Asvin G
  - Feb 16, 2022 04:30
  - Isn’t the Neron Severi group rank generically 1 and 4 only if you are a product of isogenous elliptic curves?

Propositions as Some Types and Algebraic Nonalgebraicity (15)
- Mike Shulman
  - Dec 19, 2025 17:54
  - There are many different kinds of type theory that can serve as internal languages for elementary toposes. Some of them ...
- Westlifer
  - Dec 18, 2025 07:58
  - If I understand correctly, the logic enriched type theory is often presented as a 2-layered type theory, with a universe ...
- Peter LeFanu Lumsdaine
  - Jan 16, 2012 19:33
  - On the language issue: I think it’s that “Noun1 verbs noun2” very often carries the additional implicature that noun2 is ...
- Mike Shulman
  - Jan 15, 2012 22:59
  - But I have to say, your calculator has no business telling you that e −999999e^{−999999} is 0 I don’t know ...
- Jesse C. McKeown
  - Jan 15, 2012 20:36
  - OK, exaggerating with the analytic functions with relatively large derivative was I… But I have to say, your calculator has ...