Timeline for Does the classification diagram localize a category with weak equivalences?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29 at 7:48 | answer | added | Ken | timeline score: 0 | |
| Nov 2, 2015 at 16:22 | answer | added | Aaron Mazel-Gee | timeline score: 1 | |
| Apr 4, 2012 at 17:51 | comment | added | Mike Shulman | @Jeff: Ah, were you thinking of something like Chris' answer below? | |
| Apr 4, 2012 at 16:03 | answer | added | Chris Schommer-Pries | timeline score: 10 | |
| Apr 4, 2012 at 7:12 | comment | added | Mike Shulman | @Jeff, that paper was also suggested in another answer that's since been deleted. Can you explain why knowing that N(C,W) is half of a Quillen equivalence also tells you that it is equivalent to the localization of C at W, without some sort of additional argument like the one Denis-Charles gave? | |
| Apr 4, 2012 at 6:41 | comment | added | Jeff Smith | I think the result you need is in a paper of Barwick and Kan. They show that the functor N(C,W) is half of a Quillen equivalence. | |
| Apr 3, 2012 at 21:50 | vote | accept | Mike Shulman | ||
| Apr 2, 2012 at 23:53 | answer | added | D.-C. Cisinski | timeline score: 6 | |
| Apr 2, 2012 at 21:42 | comment | added | Mike Shulman | It seems unlikely to me that Hom(I,C) could model all $(\infty,1)$-functors $I\to L(C,W)$, since you haven't applied any fibrant replacement to $(C,W)$ to make the morphisms in $W$ into equivalences. | |
| Apr 2, 2012 at 20:56 | comment | added | Thomas Nikolaus | I have been asking me this as well a while ago. I think for it is important to figure out to which extend for the given pair (C,W) and a small category I the functor category Hom(I,C) with the induced notion of weak equivalences models all maps of infinity categories $NI \to L(C,W)$. This is true for a properly behaved model category, but in general I have no idea. | |
| Apr 2, 2012 at 18:05 | history | asked | Mike Shulman | CC BY-SA 3.0 |