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    • 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 CRingop 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.

    • A class of structures similar to quantum groups.

      v1, current

    • 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(ϕ3)

      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?

    • 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

    • 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]→X from the Cartesian product [n]×[m] to a set X.

      which I have reverted back.

      diff, v12, current

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

      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 TorAb1(A,B) is a torsion group, so far for the case that A 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→Cat.

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

    • 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

    • 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

    • starting a category:reference-page in which to eventually collect pointers to the contributions to this upcoming book collection

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • We may be hearing next week about the internal logic of (∞,2)-toposes. Is there anything to say further on this page beyond what we find out at 2-topos?

      diff, v7, current

    • Started something to record today’s article

      • David Kern, Categorical spectra as pointed (∞,ℤ)-categories [arXiv:2410.02578]

      v1, current

    • a bare list of references, to be !include-ed into the References-sections of relevant entries (such as at supergeometry and fermion), for ease of synchronization

      v1, current

    • Page created, but author did not leave any comments.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have incorporated Jonas’ comment into the text at pretopos, changing the definition to “a category that is both exact and extensive”, as this is sufficient to imply that it is both regular and coherent.

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