Timeline for Difficulties with descent data as homotopy limit of image of Čech nerve
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 19, 2016 at 14:20 | vote | accept | Arrow | ||
| S Apr 19, 2016 at 14:15 | history | suggested | Arrow | CC BY-SA 3.0 |
corrected tex
|
| Apr 19, 2016 at 14:07 | review | Suggested edits | |||
| S Apr 19, 2016 at 14:15 | |||||
| Apr 19, 2016 at 13:48 | history | edited | Denis Nardin | CC BY-SA 3.0 |
Added a proof of the statement about n-cofinality
|
| Apr 19, 2016 at 12:07 | comment | added | Denis Nardin | @Arrow More precisely, the equalizer $C\rightrightarrows D$ is the category whose objects are pairs $(c,\alpha)$, where $c\in C$ and $\alpha:Fc\cong Gc$ and morphisms $(c,\alpha)\to (c',\alpha')$ are maps $c\to c'$ making the obvious square commute. If you want to discuss more details feel free to swing by the homotopy theory chatroom where I can give you more details than in these puny comment boxes | |
| Apr 19, 2016 at 12:05 | comment | added | Arrow | Thank you! I might ask this question separately in a few hours. Regarding coherent diagrams of the form $*\to C\rightrightarrows D$, they iso $\alpha :Fc\rightarrow Gc$ does not have to be natural in $c$, right? | |
| Apr 19, 2016 at 11:21 | comment | added | Denis Nardin | I think I should be able to cobble together a proof today. If anyone finds a genuine reference it will be better of course. Unfortunately I've looked in HTT, HA and Joyal's notes on quasicategories without success. (and thanks @ZhenLin for the diagram :)) | |
| Apr 19, 2016 at 10:59 | comment | added | Dylan Wilson | There is no such in HTT. I remember trying to find a reference for this and failing a while ago, but have dim memories of Lurie getting around this problem a different way... I'll see if I can find it. | |
| Apr 19, 2016 at 9:04 | comment | added | Arrow | Thank you very much for the answer. I looked in 'Higher Topos Theory' but could not find any statement of the $n$-cofinality of the inclusion Dylan Wilson mentioned (in fact I could not find a definition of $n$-cofinality, only of final maps of simplicial sets). Could you please help me with the details? | |
| Apr 19, 2016 at 6:29 | history | edited | Zhen Lin | CC BY-SA 3.0 |
added 3 characters in body
|
| Apr 19, 2016 at 0:24 | comment | added | Denis Nardin | If someone can fix the commutative diagram I will be grateful... | |
| Apr 19, 2016 at 0:23 | history | answered | Denis Nardin | CC BY-SA 3.0 |