Timeline for Homotopy excision and homotopy pushout
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2013 at 1:23 | answer | added | Peter May | timeline score: 5 | |
| Apr 10, 2013 at 21:55 | comment | added | Ricardo Andrade | @David White: I am afraid the Strom/Hurewicz model structure on topological spaces is not Quillen equivalent to the Quillen model structure. One only gets a Quillen adjunction between these model structures. | |
| Apr 10, 2013 at 21:31 | vote | accept | Fernando | ||
| Apr 10, 2013 at 21:31 | comment | added | Fernando | Perhaps, I should be more clear in question 3. When you have a excisive triad, the pushout of $(A\cap B)\to B $ along $(A\cap B)\to A $ is $X$. Thus a excisive triad may be seen as a special kind of pushout. If you have a homotopy pushout diagram, I guess you can replace for a homotopy equivalent excisive triad. So, the hypothesis of the homotopy excision may be replaced by "a homotopy pushout in which the morphisms are (n-1) equivalence and (m-1) equivalence". Then you have something about the homotopy pullbacks... .... | |
| Apr 10, 2013 at 21:30 | comment | added | Fernando | Since the inverse question - "when the homotopy pushout squares in the Quillen model are homotopy pushout squares in the Hurewicz model" - seems to have only a trivial answer, I think the question 1 should be ignored. | |
| Apr 10, 2013 at 20:55 | answer | added | Fernando Muro | timeline score: 5 | |
| Apr 10, 2013 at 20:26 | comment | added | David White | For (3) the references at the bottom of the nLab article are great: ncatlab.org/nlab/show/homotopy+limit. There was also a MO question previously asking for references for homotopy colimits: mathoverflow.net/questions/454/references-for-homotopy-colimit. I haven't read those closely enough to know if they include anything about (2), because I've never really thought about (2) before and I'm not sure it's true. Where's the cofibrant replacement in homotopy excision? | |
| Apr 10, 2013 at 20:23 | comment | added | David White | I'm not sure if this is exactly what you're seeking, but it's worth noting that these three model structures are Quillen equivalent (via the identity functor) as can be seen from the nLab article on the Strom model structure. With that in mind, this MO question gives one possible answer for your first question: mathoverflow.net/questions/82813. Does that help at all for the application you have in mind? | |
| Apr 10, 2013 at 19:58 | history | asked | Fernando | CC BY-SA 3.0 |