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    • starting page on cubical infinity-groupoids

      Anonymouse

      v1, current

    • starting page on cubical objects in simplicial sets

      Anonymouse

      v1, current

    • The entry Clifford algebra used to state the classification and Bott periodicty over the complex numbers, but not over the real numbers. I have added in now the relevant statements, straight from Lawson-Michelson:

      Just the bare statements so far.

    • At the old entry cohomotopy used to be a section on how it may be thought of as a special case of non-abelian cohomology. While I (still) think this is an excellent point to highlight, re-reading this old paragraph now made me feel that it was rather clumsily expressed. Therefore I have rewritten (and shortened) it, now the third paragraph of the Idea-section.

      (We had had long discussion about this entry back in the days, but it must have been before we switched to nForum discussion, because on the nForum there seems to be no trace of it.)

    • starting page on the opposite simplicial infinity-groupoid

      Anonymouse

      v1, current

    • starting some bare minimum (the notion in quantum information, not in Clifford algebra)

      v1, current

    • The following old material was sitting at triangulated category and was labeled “discussion”. I am hereby moving it from there to here. Probably some of it deserves to be merged into the entry in some form, but under a headline “history”.

      [begin forwarded discussion]

      The original definition of triangulated categories is apparently due to Verdier, who developed the theory upon guidelines by Grothendieck; Dold and Puppe developed independently a version without octahedron axiom with motivation in algebraic topology. In the manuscript Pursuing Stacks, Grothendieck mentions that the usual definition of triangulated categories and the corresponding derived categories seemed to be inadequate for some of the developments that he wished for. He also says something to the effect that he had tried to interest various of his ex-students in doing a thorough treatment of the ideas, which he considered to be necessary for future development, and which he then proceeds to sketch out.

      +–{+ .query} Zoran Skoda: I am not quite sure if this is entirely correct. Grothendieck indeed wanted more flexibility in homotopical algebra and went to develop these things; but if one talks only very specifically about the concept of triangulated category itself (not wider context) than the main complaint of everybody was about the crudeness of localization at quasiisomorphisms; the thing which for example Drinfel’d’s “quotients of dg-categories” paper successfully rectifies (and then again Lyubashenko in quotients of A∞-categories). =–

      That led to the theory of derivators, where the idea is that in addition to looking at a basic category of ’things’ such as chain complexes, you should also look at all categories of diagrams of such things, and the derived / homotopy Kan extensions between the corresponding derived categories that correspond to a change of the indexing category. The basic idea behind this was also explored slightly later by Alex Heller (1988). See the references on the pages derivator, pointed derivator, and stable derivator.

      [end forwarded discussion]

    • Started page on generalized symmetries, with brief description of main Idea.

      v1, current

    • a bare list of references, to be !include-ed into the References-list of relevant entries

      v1, current

    • starting page on triangulated type theory

      Anonymouse

      v1, current

    • He is no longer at Paderborn (nor at Leeds). NB his notes on the octahedral axiom are not mentioned on his web page.

      diff, v2, current

    • starting page on simplicial infinity-groupoids

      Anonymouse

      v1, current

    • starting article on point of an (infinity,1)-topos

      Anonymouse

      v1, current

    • Stone duality for coherent spaces and coherent locales.

      diff, v2, current

    • added table of contents and section headers and a related concepts section

      Anonymouse

      diff, v4, current

    • started entry on stabilization (in the sense of sending an (oo,1)-category to its free stable (infinity,1)-category)

      I want to eventually state more properties of the effect of stabilization on objects here.

    • starting page on flat distributive lattices

      Anonymouse

      v1, current

    • starting stub on Phoa’s principle

      Anonymouse

      v1, current

    • The notion of a frame in projective geometry over a field or skewfield.

      v1, current

    • It is being pointed out to me by email that this entry says about the algebra C0(X) of functions vanishing at infinity that:

      C0(X) is no longer a Banach space

      (due to revision 1 by Todd Trimble, way back in October 2009)

      This seems odd, as C0(X) is a standard example of a Banach space, unless something else is meant here.

      It seems nothing in the entry depends on this side-remark, so that it may be worth deleting.

      diff, v11, current

    • starting page on the fat Delta category

      Anonymouse

      v1, current

    • starting page on Clifford-Bianchi groups

      Anonymouse

      v1, current

    • brief category:people-entry for hyperlinking references (and edit logs!)

      v1, current

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

      v1, current

    • added this pointer:

      • C. S. Aravinda, Sudhir Rao: Speaking the language of mathematics, interview with Don Zagier, Bhāvanā mathematics magazine 7 2 (2023) [web]

      diff, v5, current

    • starting page on rigid analytic motives

      Anonymouse

      v1, current

    • starting page on Berkovich motives

      Anonymouse

      v1, current

    • created motive just in order to link to the sub-pages on this that we already have, and in order to record a link to a useful MO discussion about them.

    • This article has a weird claim on top, highlighted in yellow (see the second line):

      Redirected from “local Langlands correspondence”.

      Note: local Langlands conjecture and local Langlands conjecture both redirect for “local Langlands correspondence”.

    • starting page on the effective 2-topos

      Anonymouse

      v1, current

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