# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

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

lelf

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

• 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.

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

• 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.

• 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?

• Would like to delete content

Alex Hoffnung

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

• I added to cylinder object a pointer to a reference that goes through the trouble of spelling out the precise proof that for $X$ a CW-complex, then the standard cyclinder $X \times I$ is again a cell complex (and the inclusion $X \sqcup X \to X\times I$ 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 $X_n$, then the cells of $X_{n+1}$ glued in at top and bottom, then the further $(n+1)$-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="http://ncatlab.org/nlab/show/Bredon+cohomology">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="http://ncatlab.org/nlab/show/orbit+category">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="http://www.math.ntnu.no/~stacey/Vanilla/nForum/comments.php?DiscussionID=650&page=1">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.)

• starting something, in equivariant parallel to CW-approximation. Not much here yet, but need to save.

• A stub to fulfil a link.

• 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”.)

• 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…

• Updated the link to his webpage

• 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.

(!?)

• 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.

• Created.

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

• starting something

• 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

• 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

• 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.

HieronymousCoward

… the limit

$L c := \lim_{c\to R d} d$

over the comma category $c/R$ (whose objects are pairs $(d,f:c\to R d)$ and whose morphisms are arrows $d\to d'$ in $D$ making the obvious triangle commute in $C$) of the projection functor

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

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 $L c$ over the comma category of the projection functor $L c$”, which would be circular. But it must be that both formulas are intended as synonymous definitions of $L c$. 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 $lim$ and $colim$ 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 equivariant bundle

• 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 !?

• Created page, work in progress

• Created.

• brief category:people-entry for hyperlinking references at Elmendorf’s theorem and maybe elsewhere