Timeline for If $J$-coverings can be glued $I$-locally is $J$-locality an $I$-local property? (Reducing descent problems to simpler ones)
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2017 at 16:44 | comment | added | Marc Hoyois | I don't know. SGA4 is a good reference for basic descent theory. They use sieves as much as possible, so many proofs translate directly to higher categories. | |
| Feb 19, 2017 at 15:57 | comment | added | Saal Hardali | Thanks! This is very useful and i'm a bit surprised I never saw it mentioned anywhere. Do you have a reference culminating these kind of results (general stuff about descent theory) or is it the sort of thing one just picks up as he goes? | |
| Feb 19, 2017 at 15:55 | vote | accept | Saal Hardali | ||
| Feb 19, 2017 at 15:53 | comment | added | Marc Hoyois | And $C$ could be an ∞-category as well. | |
| Feb 19, 2017 at 15:35 | comment | added | Marc Hoyois | Yes, the same proof applies word for word for presheaves valued in any ∞-category. | |
| Feb 19, 2017 at 11:55 | comment | added | Saal Hardali | Thanks! Is this true for stacks of $\infty$-groupoids as well? It seems to me like a similar proof is possible, but i'm still learning this stuff. | |
| Feb 18, 2017 at 20:39 | history | answered | Marc Hoyois | CC BY-SA 3.0 |