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- Discussion Type
- discussion topicgame theory
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Mar 18th 2021

Over half a year later, dialed back the speculation, as discussed at https://nforum.ncatlab.org/discussion/10108/game-theory/

- Discussion Type
- discussion topicChurch numeral
- Category Latest Changes
- Started by Mike Shulman
- Comments 1
- Last comment by Mike Shulman
- Last Active Mar 18th 2021

- Discussion Type
- discussion topicAgda
- Category Latest Changes
- Started by nLab edit announcer
- Comments 6
- Last comment by Mike Shulman
- Last Active Mar 18th 2021

- Discussion Type
- discussion topicdense functor
- Category Latest Changes
- Started by David_Corfield
- Comments 8
- Last comment by JonasFrey
- Last Active Mar 18th 2021

- Discussion Type
- discussion topicclassifying topos
- Category Latest Changes
- Started by Urs
- Comments 54
- Last comment by Hurkyl
- Last Active Mar 18th 2021

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.

- Discussion Type
- discussion topicArthur Jaffe
- Category Latest Changes
- Started by Urs
- Comments 10
- Last comment by zskoda
- Last Active Mar 18th 2021

I gave the reference

- Arthur Jaffe, Frank Quinn,
*“Theoretical Mathematics”: Towards a cultural synthesis of mathematics and theoretical physics*, Bulletin of the AMS, Volume 29,Number 1, July 1993 (arXiv:math/9307227)

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.

- Arthur Jaffe, Frank Quinn,

- Discussion Type
- discussion topiccounterexamples in category theory
- Category Latest Changes
- Started by Martti_Karvonen
- Comments 20
- Last comment by Urs
- Last Active Mar 18th 2021

- Discussion Type
- discussion topicdense subcategory
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Mar 18th 2021

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).

- Discussion Type
- discussion topicTemplate page
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 18th 2021

- Discussion Type
- discussion topicequivariant Whitehead theorem
- Category Latest Changes
- Started by Urs
- Comments 13
- Last comment by Urs
- Last Active Mar 18th 2021

- Discussion Type
- discussion topicAlex Hoffnung
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Mar 18th 2021

- Discussion Type
- discussion topicTransformation Groups
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 18th 2021

- Discussion Type
- discussion topiccylinder object
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by zskoda
- Last Active Mar 17th 2021

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. )

- Discussion Type
- discussion topicBredon cohomology
- Category Latest Changes
- Started by Urs
- Comments 33
- Last comment by Urs
- Last Active Mar 17th 2021

`<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>`

- Discussion Type
- discussion topicequivariant stable cohomotopy
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 17th 2021

added references (also to

*Burnside ring*):Erkki Laitinen,

*On the Burnside ring and stable cohomotopy of a finite group*, Mathematica Scandinavica Vol. 44, No. 1 (August 30, 1979), pp. 37-72 (jstor:24491306, Laitinen79.pdf:file)Wolfgang Lück,

*The Burnside Ring and Equivariant Stable Cohomotopy for Infinite Groups*(arXiv:math/0504051)

- Discussion Type
- discussion topicequivariant stable homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Mar 17th 2021

I am slowly creating a bunch of entries on basic concepts of equivariant stable homotopy theory, such as

- equivariant suspension spectrum, equivariant sphere spectrum, equivariant homotopy groups, RO(G)-grading, fixed point spectrum, tom Dieck splitting

At the moment I am mostly just indexing Stefan Schwede’s

- Discussion Type
- discussion topicG-spectrum
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Mar 17th 2021

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.

- Discussion Type
- discussion topicG-CW complex
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 17th 2021

started

*G-CW complex*.

- Discussion Type
- discussion topicorbit category
- Category Latest Changes
- Started by Urs
- Comments 11
- Last comment by Urs
- Last Active Mar 17th 2021

added to

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

- Discussion Type
- discussion topicequivariant Hopf degree theorem
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Mar 17th 2021

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.)

- Discussion Type
- discussion topicBurnside ring
- Category Latest Changes
- Started by Todd_Trimble
- Comments 54
- Last comment by Urs
- Last Active Mar 17th 2021

I added a Definition section to Burnside ring (and made Burnside rig redirect to it).

- Discussion Type
- discussion topicG-CW approximation
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 16th 2021

starting something, in equivariant parallel to

*CW-approximation*. Not much here yet, but need to save.

- Discussion Type
- discussion topicdatabase theory
- Category Latest Changes
- Started by David_Corfield
- Comments 1
- Last comment by David_Corfield
- Last Active Mar 16th 2021

- Discussion Type
- discussion topicparametric right adjoint
- Category Latest Changes
- Started by Mike Shulman
- Comments 11
- Last comment by David_Corfield
- Last Active Mar 16th 2021

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”.)

- Discussion Type
- discussion topicproof net
- Category Latest Changes
- Started by Todd_Trimble
- Comments 16
- Last comment by nLab edit announcer
- Last Active Mar 16th 2021

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).

- Discussion Type
- discussion topicpolynomial functor
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by David_Corfield
- Last Active Mar 15th 2021

added to

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

- Discussion Type
- discussion topichomotopical algebraic quantum field theory
- Category Latest Changes
- Started by Urs
- Comments 12
- Last comment by Urs
- Last Active Mar 15th 2021

On occasion of Alexander Schenkel’s most recent talk (here) I am finally splitting off an entry

*homotopical algebraic quantum field theory*from*AQFT*.

- Discussion Type
- discussion topictwisted equivariant K-theory
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 15th 2021

- Discussion Type
- discussion topicDavid Spivak
- Category Latest Changes
- Started by Tim_Porter
- Comments 3
- Last comment by David_Corfield
- Last Active Mar 15th 2021

- Discussion Type
- discussion topicMichael Atiyah
- Category Latest Changes
- Started by Urs
- Comments 9
- Last comment by Urs
- Last Active Mar 15th 2021

- Discussion Type
- discussion topicAtiyah–Hirzebruch spectral sequence
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 15th 2021

added pointer to:

- Dale Husemöller, Michael Joachim, Branislav Jurčo, Martin Schottenloher, Section 21 of:
*Basic Bundle Theory and K-Cohomology Invariants*, Springer Lecture Notes in Physics**726**, 2008, (pdf, doi:10.1007/978-3-540-74956-1)

- Dale Husemöller, Michael Joachim, Branislav Jurčo, Martin Schottenloher, Section 21 of:

- Discussion Type
- discussion topictwisted K-theory
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Mar 15th 2021

am slowly starting to add some genuine content to twisted K-theory

- Discussion Type
- discussion topicBott periodicity
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Mar 15th 2021

have created an entry for

*Bott periodicity*

- Discussion Type
- discussion topicequivariant K-theory
- Category Latest Changes
- Started by Urs
- Comments 24
- Last comment by Urs
- Last Active Mar 15th 2021

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.

- Discussion Type
- discussion topicArf-Kervaire invariant problem
- Category Latest Changes
- Started by DavidRoberts
- Comments 7
- Last comment by Urs
- Last Active Mar 15th 2021

I fleshed out the page Arf-Kervaire invariant problem, and added a link to the new notes of HHR giving a nice introduction to the problem.

- Discussion Type
- discussion topictwisted Umkehr map
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 15th 2021

created an entry

*twisted Umkehr map*. The material now has some overlap with what I just put into*Pontrjagin-Thom collapse map*. But that doesn’t hurt, I think.

- Discussion Type
- discussion topicdifferential algebraic K-theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Mar 15th 2021

added some lines to

*differential algebraic K-theory*also a stub

*Beilinson regulator*

- Discussion Type
- discussion topicBeilinson's Conjectures on Special Values of L-Functions
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 10
- Last comment by Urs
- Last Active Mar 15th 2021

- Discussion Type
- discussion topicequivariant group
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 15th 2021

starting something, to go with and rhyme on

*equivariant principal bundle*. Not done yet, but need to save.

- Discussion Type
- discussion topicclassical double copy
- Category Latest Changes
- Started by Luigi
- Comments 16
- Last comment by Urs
- Last Active Mar 15th 2021

- Discussion Type
- discussion topicBMN matrix model
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Mar 15th 2021

- Discussion Type
- discussion topicPetri net
- Category Latest Changes
- Started by Tim_Porter
- Comments 15
- Last comment by nLab edit announcer
- Last Active Mar 14th 2021

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.

- Discussion Type
- discussion topicincarnations of rational equivariant topological K-theory -- table
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Mar 14th 2021

- Discussion Type
- discussion topicrational equivariant K-theory
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 14th 2021

am giving this its own entry, for ease of hyperlinking.

For the moment this is mostly just the table

*incarnations of rational equivariant topological K-theory – table*adjoined with some basic text around it.

- Discussion Type
- discussion topicdelocalized equivariant cohomology
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Mar 14th 2021

- Discussion Type
- discussion topicGuido Mislin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 14th 2021

brief

`category:people`

-entry for hyperlinking references at*Baum-Connes conjecture*

- Discussion Type
- discussion topicBaum-Connes conjecture
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 14th 2021

created

*Baum-Connes conjecture*with an emphasis on the*Green-Julg theorem*(of the statement in KK-theory).

- Discussion Type
- discussion topicK-Theory for Operator Algebras
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Mar 14th 2021

I have started one of those hyperlinked indices at he “reference”-entry

*K-Theory for Operator Algebras*.

- Discussion Type
- discussion topicsimplicial homotopy theory
- Category Latest Changes
- Started by Urs
- Comments 18
- Last comment by Urs
- Last Active Mar 14th 2021

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.

- Discussion Type
- discussion topicKerodon
- Category Latest Changes
- Started by nLab edit announcer
- Comments 2
- Last comment by Urs
- Last Active Mar 14th 2021

- Discussion Type
- discussion topicadjoint functor theorem
- Category Latest Changes
- Started by John Baez
- Comments 14
- Last comment by Todd_Trimble
- Last Active Mar 13th 2021

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

… 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.

- Discussion Type
- discussion topicFoling Zou
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 13th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant bundle*

- Discussion Type
- discussion topicwriter comonad
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by David_Corfield
- Last Active Mar 13th 2021

started a minimum at

*writer comonad*

- Discussion Type
- discussion topicTakao Matumoto
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 13th 2021

brief

`category:people`

-entry for hyperlinking references at*G-CW-complex*and at*equivariant Whitehead theorem*, in fact for recording these references:Takao Matumoto,

*On $G$-CW complexes and a theorem of JHC Whitehead*, J. Fac. Sci. Univ. Tokyo Sect. IA 18, 363-374, 1971Takao Matumoto, _Equivariant K-theory and Fredholm operators, J. Fac. Sci. Tokyo 18 (1971/72), 109-112 (pdf, MatumotoEquivariantKTheory.pdf:file)

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 !?

- Discussion Type
- discussion topicSlawomir Kwasik
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 13th 2021

brief

`category:people`

-entry for hyperlinking references at*equivariant Whitehead theorem*

- Discussion Type
- discussion topicaction monad
- Category Latest Changes
- Started by PaoloPerrone
- Comments 9
- Last comment by nLab edit announcer
- Last Active Mar 12th 2021

- Discussion Type
- discussion topicMath-Net.Ru
- Category Latest Changes
- Started by Dmitri Pavlov
- Comments 1
- Last comment by Dmitri Pavlov
- Last Active Mar 12th 2021

- Discussion Type
- discussion topicElmendorf's theorem
- Category Latest Changes
- Started by Urs
- Comments 20
- Last comment by Urs
- Last Active Mar 12th 2021

started

*Elmendorf’s theorem*with a brief statement of the theorem

- Discussion Type
- discussion topicdiscrete and indiscrete topology
- Category Latest Changes
- Started by Urs
- Comments 30
- Last comment by Dmitri Pavlov
- Last Active Mar 12th 2021

created discrete and codiscrete topology

- Discussion Type
- discussion topicJonathan Rubin
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Mar 12th 2021

brief

`category:people`

-entry for hyperlinking references at*Elmendorf’s theorem*and maybe elsewhere