Timeline for Questions about SGA 4
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 8, 2022 at 15:19 | vote | accept | user1022117 | ||
| Feb 8, 2022 at 6:25 | comment | added | David Roberts♦ | Continuing Tim's last comment, there are a lot of things about Grothendieck toposes, which by Giraud's theorem are more or less locally presentable pretoposes, that extend to the more general setting of loc. pres. categories, perhaps with some niceness conditions thrown in. | |
| Feb 8, 2022 at 1:37 | history | became hot network question | |||
| Feb 7, 2022 at 21:31 | answer | added | R. van Dobben de Bruyn | timeline score: 11 | |
| Feb 7, 2022 at 19:54 | comment | added | Tim Campion | Re (3): I'm not sure exactly what Joyal meant, but I believe the theory of locally presentable categories as initiated by Gabriel and Ulmer grew out of thinking about things like the Ind-categories studied in SGA 4. Certainly reading this part of SGA 4 in retrospect, one sees many of the statements as sitting in a broader context, and if one were re-writing SGA 4 today for a categorically-saavy audience, one would write a bit differently to reflect this. | |
| Feb 7, 2022 at 19:52 | comment | added | Tim Campion | Re: (1), I'm not an algebraic geometer, but if a topos has enough points, then there are a lot of questions which can be reduced to checking on stalks. One place I've seen this come up is when defining model structures on categories of simplicial pre/sheaves, where having enough points allows one to take the shortcut of defining weak equivalences stalkwise. I'm sure there are lots of other places where the ability to check a property on stalks is useful. | |
| Feb 7, 2022 at 19:09 | history | edited | YCor |
edited tags
|
|
| Feb 7, 2022 at 17:28 | history | asked | user1022117 | CC BY-SA 4.0 |