Timeline for Concrete sheaves
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2023 at 12:12 | vote | accept | NDewolf | ||
| Sep 29, 2022 at 18:57 | answer | added | Dmitri Pavlov | timeline score: 2 | |
| Sep 28, 2022 at 14:50 | comment | added | Dmitri Pavlov | Requiring V-locality makes the presheaf F trivial: its value on an object X is given by F(*)^{X(*)}, where * denotes the terminal object in the site, and F(*) denotes the set of points of F. | |
| Sep 28, 2022 at 14:38 | comment | added | NDewolf | As a follow-up question. Does it give something extra to require the concrete sheaves to also be $V$-local? Hence, have some kind of double sheaf structure. | |
| Sep 28, 2022 at 14:35 | comment | added | Dmitri Pavlov | Yes, there are two entirely different Grothendieck topologies being used here. | |
| Sep 28, 2022 at 13:56 | comment | added | NDewolf | Oh I think I see where I messed up. Sheaves are local objects with respect to the geometric morphism to the category of presheaves (on some site), which has nothing to do with the morphisms in the definition of concrete sheaves. So they are local with respect to one embedding and separated with respect to the geometric morphism $E\rightarrow S$? | |
| Sep 28, 2022 at 13:41 | comment | added | Dmitri Pavlov | Given that objects of $E$ are sheaves, the V-separated objects in E are V-separated sheaves, i.e., concrete sheaves. | |
| Sep 28, 2022 at 11:48 | history | edited | YCor |
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| Sep 28, 2022 at 11:07 | history | edited | NDewolf | CC BY-SA 4.0 |
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| Sep 28, 2022 at 10:59 | history | asked | NDewolf | CC BY-SA 4.0 |