Timeline for Is there a description of sheaf cohomology in algebraic-topological terms?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2012 at 13:21 | answer | added | Akhil Mathew | timeline score: 3 | |
| Mar 9, 2010 at 2:10 | comment | added | Omar Antolín-Camarena | @Mariano: Could you explain what you mean? Do you mean that derived functors are just the functors induced on homotopy categories by some functors on categories with weak equivalences (or more specifically, model categories)? If so (even though I didn't say), I wanted something more concrete (or "elementary") than "well, the injective resolutions you must take to compute sheaf cohomology are just cofibrant replacements in an approriate model structure". | |
| Mar 9, 2010 at 2:06 | comment | added | Omar Antolín-Camarena | @Charles Siegel: I guess I regard the simplicial Cech nerve as a construction in Algebraic Topology and you can get the usual Cech complex by Dold-Kan, but I wanted something more along the lines of "take this sort of cohomology on Y, and the map induced to cohomology on X and do this" or "build these spaces out of X and Y and take this kind of cohomology of them", etc. (I can't say precisely what description I want but I'll know it when I see it.) | |
| Mar 9, 2010 at 1:58 | comment | added | Omar Antolín-Camarena | @Mariano & Charles Siegel, both: I wasn't very explicit about what kind of constructions I wanted in the description, but I meant things like homotopy classes of maps between appropriately defined spaces (for example, ordinary cohomology), and whatever you can get from them by kernels and other such operations from homological algebra. (You may mean something like this without me realizing it, in which case I would be very grateful if you enlightened me!) | |
| Mar 9, 2010 at 1:02 | answer | added | Chris Schommer-Pries | timeline score: 8 | |
| Mar 8, 2010 at 23:39 | comment | added | Charles Siegel | As is computing the Cech Complex. | |
| Mar 8, 2010 at 22:36 | comment | added | Mariano Suárez-Álvarez | Computing derived functors is one of the common, usual constructions in Algebraic Topology! | |
| Mar 8, 2010 at 22:17 | history | asked | Omar Antolín-Camarena | CC BY-SA 2.5 |