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    • A class of structures similar to quantum groups.

      v1, current

    • created a “category: reference”-page The Stacks Project

      I have only now had a closer look at this and am impressed by the scope this has. Currently a total of 2288 pages. It starts with all the basics, category theory, commutative algebra and works its way through all the details to arrive at algebraic stacks.

      So besides my usual complaint (Why behave as if there are not sites besides the usual suspects on CRing opCRing^{op} and either give a general account or call this The Algebraic Stacks Project ? ) I am enjoying seeing this. We should have lots of occasion to link to this. Too bad that this did not start out as a wiki.

    • Added a reference to Tall–Wraith. Changed ∘:P⊗ kP→P\circ: P \otimes_k P \to P to ∘:P⊙ kP→P\circ: P \odot_k P \to P. Added redirects.

      diff, v3, current

    • created a currently fairly empty entry quantum measurement, just so as to have a place where to give a commented pointer to the article

      • Klaas Landsman, Robin Reuvers, A Flea on Schrödinger’s Cat, Found. Phys. 43, 373-407 (2013) (arXiv:1210.2353)

    • I needed an entry to be able to point to which collects pointers to the various entries on “dualities” in string theory. So I created one: duality in string theory.

    • Starting page on Tr(ϕ 3)\mathrm{Tr}(\phi^3)

      Anonymouse

      v1, current

    • Canonical bases for the (representations of) quantum groups and Lie groups.

      v1, current

    • I reverted back to

      This polynomial is an invariant of the knot, the Alexander polynomial of the knot.

      I see no reason for a strange comma before “is”. The second comma is before the appositional phrase.

      diff, v23, current

    • I have edited at Tychonoff theorem:

      1. tidied up the Idea-section. (Previously there was a long paragraph on the spelling of the theorem before the content of the theorem was even mentioned)

      2. moved the proofs into a subsection “Proofs”, and added a pointer to an elementary proof of the finitary version, here

      Notice that there is an ancient query box in the entry, with discussion between Todd and Toby. It would be good to remove this box and turn whatever conclusion was reached into a proper part of the entry.

      At then end of the entry there is a line:

      More details to appear at Tychonoff theorem for locales

      which however has not “appeared” yet.

      But since the page is not called “Tychonoff theorem for topological spaces”, and since it already talks about locales a fair bit in the Idea section, I suggest to remove that line and to simply add all discussion of localic Tychonoff to this same entry.

    • Started lift.

      weak factorization system has redirects from: lifting property, right lifting property, left lifting property, lifting problem, lifting problems.

      Would it be better to have these redirect to lift?

    • For the purposes of negative thinking, it may be useful to recognise that every ∞\infty-category has a (−1)(-1)-morphism, which is the source and target of every object. (In the geometric picture, this comes as the (−1)(-1)-simplex of an augmented simplicial set.)

      Jonathan Arnoult has pointed out on CT Zulip that this is misleading: it sounds like it implies that every ∞\infty-category is monoidal! And John Baez pointed out that the analogy to augmented simplicial sets fails because in an augmented simplicial set each 0-simplex has only one face, rather than a separate “source” and “target” that are both the same (−1)(-1)-simplex.

      I suggest we just remove this paragraph and the query box following it, since I can’t think of a way to rephrase it that would be more helpful than unhelpful. But I’m open to other suggestions.

      diff, v16, current

    • created quick stub for framed bicategory

      but my machine's battery will die any second now...

    • I added a reference on Gabriel filters on quantales.

      Very strange: version one on show had a reference on Etendues (entered by T. Holder), but when I clicked edit there was none in the edit window, just in show window. I edited and one can not see it in any history, nowhere. So there was something in show cache from 2014 which is not recorded in any history edit.

      diff, v2, current

    • starting something on the concept introduced in

      • Sergei O. Ivanov, Roman Mikhailov: A higher limit approach to homology theories, Journal of Pure and Applied Algebra 219 6 (2015) 1915-1939 [arXiv:1309.4920, doi:10.1016/j.jpaa.2014.07.016]

      • Sergei O. Ivanov, Roman Mikhailov: Higher limits, homology theories and fr\mathbf{fr}-codes, in: Combinatorial and Toric Homotopy, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore (2017) 229-261 [arXiv:1510.09044, doi:10.1142/9789813226579_0004]

      but for the moment there is little more than these references

      v1, current

    • Added reference to Bruce Bartlett’s thesis.

      diff, v5, current

    • Add a strengthening of the coherence result, also due to Power.

      diff, v7, current

    • starting page on surfaceology

      Anonymouse

      v1, current

    • Explained how to prove the commutativity of addition in EFA

      diff, v11, current

    • I gave Fourier-Mukai transform a bit of an Idea-section. It overlaps substantially with the Definition section now, but I thought one needs to say the simple basic idea clearly in words first. Also added a few more pointers to literature.

    • Anonymous “helpfully” changed the statement

      A matrix is a list of lists.

      to

      A matrix is a function M:[n]×[m]→XM:[n]\times[m]\rightarrow X from the Cartesian product [n]×[m][n]\times[m] to a set XX.

      which I have reverted back.

      diff, v12, current

    • a minimum of an Idea-section, but mainly to record some references

      v1, current

    • I added a clearer “The idea” section for Adams operation, and changed the word “functorial” to “natural” in a number of places, because while various sources do say the Adams operations are functorial, they must really be natural transformations from the functor K:Top→AbGpK: Top \to AbGp to itself.

      diff, v10, current

    • a stub entry, for the moment just to make the link work

      v1, current

    • Pointed out that the ring of big Witt vectors is represented by the free lambda-ring on one generator (no coincidence; this follows by easy abstract nonsense).

      diff, v32, current

    • have now spelled out at Tor in simple terms how Tor 1 Ab(A,B)Tor_1^{Ab}(A,B) is a torsion group, so far for the case that AA is finite.

    • added to equalizer statement and proof that a category has equalizers if it has pullbcks and products

    • brief category:people-entry for hyperlinking references

      v1, current

    • Rename the page to reflect the fact that coherence and strictification are distinct, but related, theorems.

      diff, v7, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have added

      • Paolo Facchi, Giovanni Gramegna, Arturo Konderak, Entropy of quantum states (arXiv:2104.12611)

      and added publication details to

      • A. P. Balachandran, T. R. Govindarajan, Amilcar R. de Queiroz, A. F. Reyes-Lega, Algebraic approach to entanglement and entropy, Phys. Rev. A 88, 022301 (2013) (arXiv:1301.1300)

      and grouped together more discernibly the references on operator-algebraic entropy

      diff, v50, current

    • added at core the remark that the core is right adjoint to the forgetful functor Grpd→CatGrpd \to Cat.

    • felt the desire to have an entry on the general idea (if any) of synthetic mathematics, cross-linking with the relevant examples-entries.

      This has much room for being further expanded, of course.

    • The Idea-section at quasi-Hopf algebra had been confused and wrong. I have removed it and written a new one.

    • added various references, notably on computation of graviton scattering amplitudes.

      diff, v15, current

    • a minimum entry, for the moment just so as have a place to record the fact that two smooth functions are smoothly homotopic as soon as they are (continuously) homotopic

      (It sure feels like we must have recorded this somewhere already, but I couldn’t find it…)

      v1, current

    • Adding reference

      • Peter Freyd, Algebraic real analysis, Theory and Applications of Categories, Vol. 20, 2008, No. 10, pp 215-306 (tac:20-10)

      Anonymous

      diff, v8, current

    • This is a page for Sridhar Ramesh’s notion of introspective theory. Precise definitions to be added.

      Aaron David Fairbanks

      v1, current

    • starting a category:reference-entry.

      Just a single item so far, but this entry should incrementally grow as more preprints appear (similar to what we have been doing at Handbook of Quantum Gravity and similar entries).

      I know that a soft deadline for submissions of at least one of the sections is this December, so I am guessing this is planned to appear in 2024.

      v1, current

    • Have added pointer to:

      • Adam Caulton: Is a particle an irreducible representation of the Poincaré group? [arXiv:2410.02354]

      (but I haven’t more than skimmed it and don’t mean to endorse it).

      diff, v12, current

    • Added remark on geometric realizations of pairs of adjoint functors

      Roman T

      diff, v17, current

    • some minimum, for the moment just to address the issue raised in another thread, here

      v1, current

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