Timeline for Acyclic categories related to structures in algebraic topology
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 25, 2012 at 15:19 | comment | added | Patricia Hersh | @Peter: Thank you. I've just discovered that Tom Leinster has written papers on Moebius Inversion for Categories. So I guess some things are written down. | |
| Jul 29, 2012 at 3:28 | comment | added | Jonathan Chiche | As for the Quillen equivalence between the category of small categories and the category of simplicial sets, the standard references include Fritsch and Latch "Homotopy inverses for nerve" and Thomason's "Cat as a closed model category". Another reference is Cisinski's Astérisque "Les préfaisceaux comme modèles des types d'homotopie". However, while the Quillen adjunction is beautifully explained by Thomason, the Quillen equivalence part is somewhat less clear. Cisinski's Master's thesis might (I do not have it handy) explain the details, but it is not publicly available as far as I know. | |
| Jul 27, 2012 at 17:55 | comment | added | Peter May | Roman, it was Thomason, not Quillen who used it. Jonathan, I've answered your question, if only with an advertisement for a book I'm writing. Patricia, I like your answer. There is no really good reference yet, to my mind, since there is much more of interest to be said than is in any published reference. As an aside, I'd like to put in a good word for your first reference, Babson and Kozlov: that explains when you can hope that the nerve functor on categories with G-actions commutes with colimits, such as passage to orbits. That came up in recent work on equivariant classifying spaces. | |
| Jul 27, 2012 at 10:07 | comment | added | Jonathan Chiche | I have (prompted by Peter May's answer) posted a question related to this construction, see mathoverflow.net/questions/103281/…. | |
| Jul 27, 2012 at 7:08 | vote | accept | Roman Bruckner | ||
| Jul 27, 2012 at 7:15 | |||||
| Jul 27, 2012 at 7:08 | comment | added | Roman Bruckner | Yes, I'm already aware of the notion of a subdivision of a small category. However, I didn't know it was used by Quillen that way. @Patricia: Matias L. Del Hoyo, "On The Subdivision of Small Category" would be a good reference to learn about the subdivision of a small category | |
| Jul 27, 2012 at 2:39 | comment | added | Patricia Hersh | Is there a good reference for this? Thanks! | |
| Jul 27, 2012 at 2:23 | history | answered | Peter May | CC BY-SA 3.0 |