The n-Category Café

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Calendar

October 2025's Entries

• Applied Category Theory 2026
  • Oct 27, 2025
  • Applied Category Theory 2026 is taking place 6–10 July in Tallinn, Estonia, and it’s preceded by the Adjoint School Research Week, 29 June – 3 July.
• A Complex Qutrit Inside an Octonionic One
  • Oct 6, 2025
  • I’m trying to better characterize two maximal subgroups of the group of automorphisms of the exceptional Jordan algebra, whose intersection is the Standard Model gauge group.

Random Past Entries

• TeXnical Issues
  • September 2, 2006
  • Sage advice on viewing this blog and posting comments thereon.
• Functional Equations IV: A Simple Characterization of Relative Entropy
  • Feb 28, 2017
  • Relative entropy is almost uniquely characterized by the chain rule.
• Poisson-Sigma Models, Lie Algebroids, Deformations and Higher Analogues in Vienna
  • Mar 16, 2007
  • Announcement of ESI Workshop on Lie Algebroids in Summer 2007.
• The Quantum Whisky Club
  • May 28, 2010
  • Fun at Oxford.
• Freed on Higher Structures in QFT, I
  • Sep 12, 2006
  • Freed’s old observation that n-dimensional QFT assigns (n-d)-Hilbert spaces to d-dimensional volumes.
• Nonabelian Cohomology in Three (∞,1)-Toposes
  • May 26, 2010
  • On nonabelian sheaf cohomology with constant coefficients in petit and gros (oo,1)-toposes.

Recent Comments

• Applied Category Theory 2026 (1)
  • Tom Leinster
    • Oct 27, 2025 22:29
    • That program committee is bigger than half the conferences I’ve been to.

• Equivalence via Surjections (39)
  • Tim Campion
    • Oct 19, 2025 15:36
    • Another way to look at it: Say C is a nice category equipped with a notion of equivalence and a ...
  • Tim Campion
    • Oct 19, 2025 15:20
    • I guess this example (or already the example of 2-categories) illustrates another point about this: if every object is cofibrant, ...
  • Timothy Campion
    • Oct 19, 2025 15:16
    • Another example in this paradigm is an n-equivalence of topological spaces, which is an isomorphism on π ≥n+1\pi_{\geq n+1} and ...
  • Alexander Campbell
    • Oct 8, 2025 10:12
    • Necessarily the “coinductive” weak equivalences, because these are the weak equivalences in the unique model structure on the category of ...
  • Tim Campion
    • Oct 8, 2025 02:58
    • How does this play out for strict omega-categories? “strict surjective equivalence” sounds like the same thing as a folk trivial ...

• Relational Universal Algebra with String Diagrams (2)
  • Matt
    • Oct 14, 2025 19:12
    • It seems to me that this but needs editing, but I’m not sure what word is perhaps missing: “This two ...
  • John Baez
    • Sep 5, 2022 20:35
    • Nice! It’s not at all important, but I’m don’t remember hearing the word “inequation” — the people I know seem ...

• Universe Polymorphism and Typical Ambiguity (12)
  • Mike Shulman
    • Oct 14, 2025 17:02
    • The words “polymorphism” and “homomorphism” are basically unrelated.
  • Matt
    • Oct 14, 2025 16:09
    • I’m interested in the relationship of this topic to classical Algebra and to universal algebra; however, I don’t see here ...
  • Mike Shulman
    • Dec 11, 2012 16:43
    • Okay, I think I get what you’re saying. NF is one thing that might result if you start from a ...
  • Zhen Lin
    • Dec 11, 2012 09:10
    • Hmmm. Perhaps I was not clear. Essentially, NF is the _result_ of extracting the typically ambiguous fragment of Russellian type ...
  • Mike Shulman
    • Dec 11, 2012 02:09
    • In the systems I was writing about, there are many different universes, and when we write Type:TypeType:Type its meaning is ...

• Group Cohomology and Homotopy Fixed Points (3)
  • Dean Young
    • Oct 12, 2025 20:03
    • Wow thanks so much professor Baez! I may not have realized this without your post. I know I’ve been struggling ...
  • John Baez
    • Apr 30, 2020 17:33
    • Thanks! Yes, Noether. I’ve decided to improve this paragraph: And this is called Hilbert’s Theorem 90. It’s a famous result ...
  • Mathlog
    • Apr 30, 2020 17:02
    • It looks like Andreas Speiser did that in 1919. did that in 1933. There is something missing, presumably the name ...

• A Complex Qutrit Inside an Octonionic One (4)
  • John Baez
    • Oct 7, 2025 17:41
    • Okay, now I’m following the logic. Yes, that would be another brilliant insight-free proof. (At least for me, since I’d ...
  • John Baez
    • Oct 7, 2025 16:54
    • I wrote: I know the subgroup of F 4\mathrm{F}_4 that fixes e 1,e 2,e 3e_1, e_2, e_3 contains Spin(8)\text{Spin}(8). I ...
  • John Baez
    • Oct 7, 2025 16:45
    • Theo wrote: Doesn’t Part 1 follow from the statements “Yokota shows [(SU(3)×SU(3))/ℤ 3(SU(3) \times SU(3)) / \mathbb{Z}_3] preserves the standard ...
  • Theo Johnson-Freyd
    • Oct 6, 2025 20:18
    • There is a result due to Kac that reads off the classification of (conjugacy classes of) torsion elements of adjoint ...

• A Shadow of Triality? (14)
  • John Baez
    • Sep 28, 2025 11:02
    • Here are some more details on how Conway and Smith get from triality to this fact: if cc is an ...
  • John Baez
    • Sep 26, 2025 09:21
    • Ben wrote: They define an inverse loop (p. 83) and show that any inverse loop will satisfy xyz=yzx=zxy=1x y z=y ...
  • John Baez
    • Sep 25, 2025 12:59
    • Wow, this could be the really beautiful explanation I’d been hoping for! Thanks! I’d been trying to read Conway and ...
  • Ben
    • Sep 24, 2025 15:04
    • I think the answer (or something close to it) turns out to be in Conway and Smith’s On Quaternions and ...
  • John Baez
    • Sep 16, 2025 18:51
    • I got some help from Vít Tuček on MathOverflow. He pointed out that Yokota gave a proof that all inner ...

• Safeguarded AI Meeting (10)
  • David Roberts
    • Sep 4, 2025 06:26
    • In all cases, the line-by-line proof details presented here were constructed by the author. It seems important to point out ...
  • Jeffery Winkler
    • Sep 3, 2025 06:55
    • Here is a physics paper partially written using ChatGPT. https://arxiv.org/pdf/2508.21276 This will be more common in the future. Is this ...
  • Jeffery Winkler
    • Sep 3, 2025 06:27
    • Here are some more links about the connections between physics and AI. Physics Today - Nobel Prize https://pubs.aip.org/physicstoday/article-abstract/77/12/12/3320663/Nobel-Prize-highlights-neural-networks-physics 2 Physics ...
  • Jeffery Winkler
    • Aug 20, 2025 16:55
    • In 1954, Frederick Brown wrote a science fiction story titled “The Answer”. It’s so short I can reproduce it here. ...
  • Matteo Capucci
    • Aug 18, 2025 07:15
    • I quote the comment I left on John’s blog about this: I’m part of SGAI and I believe this is ...

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