Timeline for Is dgCat a category or a 2-category?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 20, 2015 at 1:58 | vote | accept | Zhaoting Wei | ||
| Sep 29, 2015 at 20:11 | comment | added | Fernando Muro | @QiaochuYuan the fact is that dgCat is what you call a strict 2-category, and hence has an underlying category. | |
| Sep 29, 2015 at 16:18 | comment | added | Qiaochu Yuan | @Fernando: well, this is a bit tricky. It's true that a strict 2-category has an underlying category given by forgetting 2-morphisms, but I prefer to use a convention where n-category always means the weak thing by default, so with that convention, if you just forget 2-morphisms composition might fail to be associative (and in any case this operation doesn't respect equivalences of 2-categories). The model-independent thing to do is to take the homotopy category, but using the word "are" for this construction seems like sweeping something under the rug. | |
| Sep 29, 2015 at 10:57 | answer | added | Ilias A. | timeline score: 11 | |
| Sep 29, 2015 at 7:42 | answer | added | AAK | timeline score: 10 | |
| Sep 29, 2015 at 6:31 | comment | added | Zhen Lin | At least if you use "2-category" in the Australian sense... | |
| Sep 29, 2015 at 6:26 | comment | added | Fernando Muro | You're aware that 2-categories are also ordinary categories, right? | |
| Sep 29, 2015 at 5:14 | comment | added | Qiaochu Yuan | Model structures present $(\infty, 1)$-categories, but there should be more structure here than that. | |
| Sep 29, 2015 at 5:01 | comment | added | Zhaoting Wei | @QiaochuYuan Is the Dwyer-Kan model structure has a interpretation in that $(\infty,2)$-category structure? | |
| Sep 29, 2015 at 4:58 | comment | added | Qiaochu Yuan | It's an $(\infty, 2)$-category. | |
| Sep 29, 2015 at 4:45 | history | asked | Zhaoting Wei | CC BY-SA 3.0 |