Timeline for Homotopy limits of quasi-categories
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 8, 2012 at 22:18 | vote | accept | Lennart Meier | ||
| Apr 25, 2012 at 8:08 | comment | added | Lennart Meier | @Spice the Bird: Yes. I have edited my question correspondingly. @Dylan: At the end, you still have to identify the homotopy limit in simplicial categories with the homotopy limit in model categories defined above, which is probably non-trivial. At least, there should be an issue about homotopy coherence vs. strict diagrams. @Fedotov: I will think about this. | |
| Apr 24, 2012 at 18:26 | answer | added | Chris Schommer-Pries | timeline score: 8 | |
| Apr 24, 2012 at 17:21 | comment | added | Dylan Wilson | Somewhere in there lies an answer to your question, since at the end of the day a homotopy limit of the simplicially enriched model categories will correspond to a homotopy limit of some ordinary simplicially enriched categories... But I may be spouting nonsense. | |
| Apr 24, 2012 at 17:20 | comment | added | Dylan Wilson | (contd) corresponds to a homotopy (co)limit of simplicially enriched categories. | |
| Apr 24, 2012 at 17:19 | comment | added | Dylan Wilson | In general, if we have a (say, presentable, or simplicially enriched) model category, then a (co)limit (in the $\infty$-categorical sense) of a diagram in the underlying infinity-category corresponds to a homotopy (co)limit in the model category. Since the category of simplicially enriched categories with the Bergner model structure is Quillen equivalent to the category of simplicial sets with the Joyal model structure, the underlying $\infty$-categories are equivalent. So an $\infty$-categorical (co)limit of $\ifnty$-categories corresponds to a homotopy colimit of simplicial sets which | |
| Apr 24, 2012 at 16:13 | history | edited | Lennart Meier | CC BY-SA 3.0 |
added 36 characters in body
|
| Apr 24, 2012 at 14:55 | comment | added | Ilias A. | May be I'm wrong, but it seems to me that it should be: $Map(N(EG),N\mathbf({\mathcal{M}}^{\circ}))^{G}$ equivalent to $N((RHom(EG,\mathcal{M})^{G})^{\circ})$, where RHom is the right derived internal Hom functor defined by B.Toën for $\mathrm{Ho}(\mathbf{Cat}_{\Delta})$. | |
| Apr 24, 2012 at 14:06 | comment | added | Spice the Bird | I am guessing that $\Omega$ means loop space? | |
| Apr 24, 2012 at 13:22 | history | asked | Lennart Meier | CC BY-SA 3.0 |