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    • Created semi-simplicial set, mainly as a repository for some terminological remarks. I would welcome anyone more knowledgeable about the history to correct or improve it!

    • starting a minimum, for the moment just to have a place for recording references

      v1, current

    • brief category:people-entry for hyperlinking references

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    • brief category:people-entry for hyperlinking references

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    • added to group cohomology

      • in the section structured group cohomology some remarks about how to correctly define Lie group cohomology and topological group cohomology etc. and how not to

      • in the section Lie group cohiomology a derivation of how from the right oo-categorical definition one finds after some unwinding the correct definition as given in the article by Brylinski cited there.

      it's late here and I am now in a bit of a hurry to call it quits, so the proof I give there may need a bit polishing. I'll take care of that later...

    • I added some basic explanatory stuff to the "Idea" section of localization. The simple idea of localizing a commutative ring really does, I think, correspond to some fancier operation you can do in topos theory (namely the topos of sheaves on the spectrum of that ring?). So, someone should try to explain that... but I can't.

      Someone should also add links from "localization" to various fancier pages on fancier kinds of localization. I did so for Bousfield localization. I also added a bit more explanation to that page.

      (I think my job at the nLab is to make pages easier for beginners to follow. This is a gargantuan, almost hopeless task... but I don't see anything else I'm dying to do here. So I'll just do a little. It makes sense for me to add more explanation to an nLab page whenever I plan to cite it on This Week's Finds.)
    • I thought it might be good if somebody explained the relationship between decategorification and extended TQFT. My understanding from talking to physicists is that you should multiply your space by $S^1$; is this right in a mathematical sense? I've added a query box asking roughly the same thing.

      Also, I attempted to add a sidebar, mostly just to try it out, and somehow it's not rendering right. Anyone want to explain what I did wrong?

    • brief category:people-entry for hyperlinking references

      v1, current

    • started to add to internalization a list of links to examples. Probably we have much more.

    • I made some very minor changes to the introduction at descent. I hesitate to do more but at present the discussion does not seem that readable to me. Can someone look at it to see what they think? The intro seems to plunge in deep very quickly and so the ‘idea’ of descent as that of gluing local information together, does not come across to me. The article is lso quite long and perhaps needs splitting up a bit.

    • I noticed that there was no entry quotient stack, so I quickly started one, just to be able to point to it from elswhere.

    • brushed up the definition at algebraic stack following the Stacks project text..

    • brief category:people-entry for hyperlinking references

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    • brief category:people-entry for hyperlinking references

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    • somebody asked me for the proof of the claim at canonical topology that for a Grothendieck topos H\mathbf{H} we have HSh can(H)\mathbf{H} \simeq Sh_{can}(\mathbf{H}).

      I have added to the entry pointers to the proof in Johnstone’s book, and to related discussion for \infty-toposes. Myself I don’t have more time right now, but maybe somebody feels inspired to write out some details in the nLab entry itself?

    • I have added at HomePage in the section Discussion a new sentence with a new link:

      If you do contribute to the nLab, you are strongly encouraged to similarly drop a short note there about what you have done – or maybe just about what you plan to do or even what you would like others to do. See Welcome to the nForum (nlabmeta) for more information.

      I had completly forgotton about that page Welcome to the nForum (nlabmeta). I re-doscivered it only after my recent related comment here.

    • added to locally ringed topos the characterization as algebras over the geometric theory of local rings.

      I give pointers to two references that I know which say this more or less explicitly: Johnstone and Lurie. But I lost the page where Johnstone says this. I had it a minute ago, but then somebody distracted me, and now it is as if the paragraph has disappeared…

    • I was talking to an ex-Adelaide student now at Oxford about some technicalities they were trying to track down regarding locally ringed spaces. I checked locally ringed topological space, and found the Stacks Project reference was out of date. I replaced it with a link to the specific tag for the definition, at least.

    • Fixed Stacks Project link to point to tag, not overall pdf nor GitHub repo by section number.

      diff, v13, current

    • I fixed a mistake at complement (where it said complements are unique), and added more to Related Concepts.

    • brief category:people-entry for hyperlinking references

      v1, current

    • I have added pdf-links to the reference

      and promoted this to the top of the list, since I suppose this is the most comprehensive account that a reader might want to go to first. Will also edit accordingly at topological stack

      diff, v18, current

    • brief category:people-entry for hyperlinking references

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


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    • brief category:people-entry for hyperlinking references

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    • I am moving the following old query box exchange from orbifold to here.

      old query box discussion:

      I am confused by this page. It starts out by boldly declaring that “An orbifold is a differentiable stack which may be presented by a proper étale Lie groupoid” but then it goes on to talk about the “traditional” definition. The traditional definition definitely does not view orbifolds as stacks. Neither does Moerdijk’s paper referenced below — there orbifolds form a 1-category.

      Personally I am not completely convinced that orbifolds are differentiable stacks. Would it not be better to start out by saying that there is no consensus on what orbifolds “really are” and lay out three points of view: traditional, Moerdijk’s “orbifolds as groupoids” (called “modern” by Adem and Ruan in their book) and orbifolds as stacks?

      Urs Schreiber: please, go ahead. It would be appreciated.

      end of old query box discussion

    • at additive functor there was a typo in the diagram that shows the preservation of biproducts. I have fixed it.

      Also formatted a bit more.

    • brief category:people-entry for hyperlinking references

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    • brief category:people-entry for hyperlinking references

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    • I was looking again at this entry, while preparing my category theory notes elsewhere, and I find that this entry is really bad.

      With the co-Yoneda lemma in hand (every presheaf is a colimit of representables, and that is dealt with well on its page), the statement of free cocompletion fits as an easy clear Idea into 2 lines, and as a full proof in maybe 10.

      The entry should just say that!

      Currently the section “technical details” starts out right, but somehow forgets along the way what it means to write a proof in mathematics.

      On the other hand, the section “Gentle introduction” seems to be beating about the bush forever. Does this really help newbies?

      diff, v54, current

    • I have split off from holographic principle and then expanded a good bit a few paragraphs on

      AdS3-CFT2 and CS-WZW correspondence

      together with a few commented references, trying to amplify how this case is given by an actual well-known theorem and at the same time seems to be generic for the more general cases of AdS-CFT which are currently much more vague.

    • The paper “Left determined model categories” is published

      Philippe Gaucher

      diff, v3, current

    • Where the example of monadic functors creating limits is mentioned, there should be a reference, at least.

      I have added pointer to MacLane 71, Exercise IV.2.2 (p. 138)

      Scanning through Borceux II, I don’t spot the statement there. (?)

      diff, v13, 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.

    • I keep wanting to point to properties of the terminal geometric morphism. While we had this scattered around in various entries (such as at global sections, at (infinity,1)-topos and elsewhere – but not for instance at (infinity,1)-geometric morphism) I am finally giving it its own entry, for ease of hyperlinking.

      So far this contains the (elementary) proofs that the geometric morphism to the base SetSet/Grpd Grpd_\infty is indeed essentially unique, and that the right adjoint is equivalently given by homs out of the terminal object.

      v1, current

    • Created:

      Wolfgang Rump is a mathematician working at the University of Stuttgart.

      He got his PhD degree in 1978 from the University of Stuttgart, advised by Klaus Wilhelm Roggenkamp.

      Selected writings

      • Wolfgang Rump, Almost abelian categories, Cahiers de topologie et géométrie différentielle catégoriques, tome 42, no 3 (2001), p. 163–225. numdam.

      v1, current

    • Just to say that I will be on family vacation until \sim Aug 7.

      It looks like we’ll have no WiFi on that house boat, so that I’ll not be able to reply here as usual. But I may try to hack myself into the Matrix via phone, from time to time.

      diff, v91, current

    • brief category:people-entry for hyperlinking references

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