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added pointer to:
Eugene P. Wigner Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren, Springer (1931) [doi:10.1007/978-3-663-02555-9, pdf]
Eugene P. Wigner, Group theory: And its application to the quantum mechanics of atomic spectra, 5, Academic Press (1959) [doi:978-0-12-750550-3]
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 -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]
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splitting the content about coherent locales from coherent space to its own article
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added at Leech lattice a pointer to
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.
brief category:people-entry for hyperlinking references at domain theory and mathematics presented in HoTT
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It is being pointed out to me by email that this entry says about the algebra of functions vanishing at infinity that:
is no longer a Banach space
(due to revision 1 by Todd Trimble, way back in October 2009)
This seems odd, as 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.
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removing old comment in query box
+– {: .query} Madeleine Birchfield: Wouldn’t an ordinal number be an object of the decategorification of the category of well-ordered sets, just as a natural number is an object of the decategorification of the category FinSet? =–
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Author of a paper mentioned at marked extensional well-founded order
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Idea at Donaldson-Thomas invariant, hopefully correct to zeroth approximation, but not sure. Related update of Dominic Joyce.
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”.
I added the remark that the canonical model structure on Cat is the model structure obtained by transferring the projective model structure on bisimplicial sets.
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for hyperlinking references at premodel category