Timeline for Resolutions by Adapted Class of Objects and Model Categories
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2011 at 20:39 | comment | added | Chris Schommer-Pries | (cont). ... F extends to a simplicial functor from the Hammock localization of the sub-category of "adapted resolutions" of C into the hammock localization of D. The composite FQ isn't a point-set level derived functor, but it should be a good analog when the point set level derived functor might not exist or when you can't get an honestly functorial Q. | |
| Dec 24, 2011 at 20:36 | comment | added | Chris Schommer-Pries | @ Justin. You are right. I don't think we should expect there to exist such a Q as a functor at the level of C, just as we should not expect there to exist "point-set level" derived functors. However I think there is a remedy for this. (I'm just speculating right now, if you know a better answer I'd love to hear it). I think there does always exist a functor Q from C into the full sub-simplicial category of the Hammock localization of C spanned by the adapted resolutions. Moreover F is homotopical when restricted to this subcategory, so extends to a map from the ... (cont) | |
| Dec 24, 2011 at 7:52 | comment | added | Justin Noel | Should we always expect that we can take strictly functorial replacements with respect to a class of objects adapted to $F$? | |
| Dec 23, 2011 at 19:47 | comment | added | Chris Schommer-Pries | This looks exactly right to me. In the case at hand Q should be the "replace by adapted class resolution" functor. | |
| Dec 23, 2011 at 17:30 | history | answered | Emily Riehl | CC BY-SA 3.0 |