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

      v1, current

    • Moved the reference to the Lawvere commentary on Isbell to ’References’.

      diff, v16, current

    • edited classifying topos and added three bits to it. They are each marked with a comment "check the following".

      This is in reaction to a discussion Mike and I are having with Richard Williamson by email.

    • I gave the reference

      the following commentary-line:

      for historical context see Hitchin 20, Sec. 8

      I admit that I only fully grasp this now, that Jaffe-Quinn’s article was in response to Atiyah’s influence on mathematics in whose wake Witten received the Fields medal.

      diff, v4, current

    • Started the page inspired by a discussion on zulip. If this is not deemed interesting enough, feel free to remove.

      v1, current

    • I have tried to brush up the entry dense subcategory a little

      (moved the references to the References, moved the part that alluded to the application with nerves to its own section and expanded slightly, added the relevant back-links).

    • Slightly modernized this page, mostly bringing in the new LaTeX-style syntax for Definition/Proposition/Proof-environments.

      diff, v19, current

    • fixed the pointers to alleged proofs of the equivariant Whitehead theorem.

      What is a canonical citation for this statement, for the unstable case, citable as an actual proof? Is it due to Bredon? Is it in his book?

      diff, v3, current

    • a category:reference-entry on tom Dieck’s book of that title

      v1, current

    • I added to cylinder object a pointer to a reference that goes through the trouble of spelling out the precise proof that for XX a CW-complex, then the standard cyclinder X×IX \times I is again a cell complex (and the inclusion XXX×IX \sqcup X \to X\times I a relative cell complex).

      What would be a text that features a graphics which illustrates the simple idea of the proof, visualizing the induction step where we have the cylinder over X nX_n, then the cells of X n+1X_{n+1} glued in at top and bottom, then the further (n+1)(n+1)-cells glued into all the resulting hollow cylinders? (I’d like to grab such graphics to put it in the entry, too lazy to do it myself. )

    • This comment is invalid XML; displaying source. <p>I added three more references to <a href="">Bredon cohomology</a>.</p> <p>two of them, by H. Honkasolo, discuss a sheaf-cohomology version of Bredon cohomology, realized as the cohomology of a topos built from the <a href="">orbit category</a>.</p> <p>It's too late for me today now to follow this up in detail, but I thought this might be of interest in the light of our discussion at <a href="">G-equivariant stable homotopy theory</a>.</p>
    • I am touching various entries related to equivariant stable homotopy theory, adding basics from the literature. For instance I briefly added to G-spectrum the basic definition via indexing on a universe, and added the statement of the equivariant stable Whitehead theorem, cross-linked with the relevant bits at equivariant homotopy theory, etc. I have also been expanding a little more at RO(G)-grading and cross-linked more with old material at equivariant cohomology. Tried to make the link between RO(G)-grading and equivariant suspension isomorphism more explicit.

      Just in case you are watching the logs and are wondering. I am not announcing every single edit, unless there is anything noteworthy.

    • added to orbit category a remark on what the name refers to (since I saw sonebody wondering about that)

    • am finally splitting this off from Hopf degree theorem, to make the material easier to navigate. Still much room to improve this entry further (add an actual Idea-statement to the Idea-section, add more examples, etc.)

      v1, current

    • Added alternative terminology “local right adjoint” and “strongly cartesian monad” from Berger-Mellies-Weber. They claim the former “has become the more accepted terminology” than “parametric right adjoint”; does anyone know other references to support this? (I think it’s certainly more logical, in that it fits with the general principle of “local” meaning “on slice categories” — not to be confused with the different general principle of “local” meaning “in hom-objects”.)

      diff, v8, current

    • There has been a pretty massive expansion at proof net. All who are interested in this are invited to have a look (but the nLab is super-slow in loading now from where I write).

      Noam Z., if you are reading this: I had looked at the notes you kindly mentioned to me recently. Could you comment on what the connection might be with the sequentialization result (see the remark 2 under theorem 1 in proof net)? The outline of proof reminded me of your description of inversion and focusing, but I confess I had a little trouble following everything (my fault, not yours).

    • added to polynomial functor the evident but previously missing remark why it is called a “polynomial”, here.

    • finally splitting this off, for ease of organizing references. Not much here yet…

      v1, current

    • changed “an English mathematician of Egyptian origin” to “a British-Lebanese mathematician”.

      In checking his “origin” on Wikipedia…

      …I see that Wikipedia says that Sir Michael Atiyah has died. Today.


      diff, v6, current

    • added to equivariant K-theory comments on the relation to the operator K-theory of crossed product algebras and to the ordinary K-theory of homotopy quotient spaces (Borel constructions). Also added a bunch of references.

      (Also finally added references to Green and Julg at Green-Julg theorem).

      This all deserves to be prettified further, but I have to quit now.

    • Hello, I thought that a new entry would be a good thing. Just a sketch for now.

      v1, current

    • I have created a stub for this at Petri net. I hope to develop the links with higher dimensional automata and also with linear logic.

    • a bare table, to be !include-ed into relevant entries.

      This is to show at a glance how various definitions used in the literature are all equivalent incarnations of rational equivariant K-theory

      v1, current

    • the definition, and highlighting that this coincides with Chen-Ruan cohomology of the global quotient orbifold, and with Bredon cohomology with coefficients in the representation ring functor

      v1, current

    • I felt we were lacking an entry titled simplicial homotopy theory that usefully collects the relevant entries that we do have. So I am starting one.

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


      v1, current

    • I fixed a trivial typo in adjoint functor theorem but left wondering about this:

      … the limit

      Lc:=lim cRdd L c := \lim_{c\to R d} d

      over the comma category c/Rc/R (whose objects are pairs (d,f:cRd)(d,f:c\to R d) and whose morphisms are arrows ddd\to d' in DD making the obvious triangle commute in CC) of the projection functor

      Lc=lim (c/RD). L c = \lim_{\leftarrow} (c/R \to D ) \,.

      I don’t really understand this (and while I could figure it out, it’s probably not good to make readers do so). At first it sounds like someone is saying “the limit LcL c over the comma category of the projection functor LcL c”, which would be circular. But it must be that both formulas are intended as synonymous definitions of LcL c. At that point one is left wondering why one has a backwards arrow under it and the other does not. I guess old-fashioned people prefer writing limits with backwards arrows under them, so someone is trying to cater to all tastes? I think it’s better in this website to use limlim and colimcolim for limit and colimit.

      I could probably guess how to fix this, but I won’t since I might screw something up.

    • brief category:people-entry for hyperlinking references at G-CW-complex and at equivariant Whitehead theorem, in fact for recording these references:

      I am not sure if I am correctly identifying webpages related to this author:

      The MathsGenealogy page here would plausibly be the correct one – except that it lists a PhD in 1976, while the articles above – which seem to be the author’s main results – are from 1971 !?

      v1, current