Timeline for Are cohomology functors sheaves?
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 20, 2020 at 15:27 | vote | accept | Praphulla Koushik | ||
| S Jul 14, 2020 at 12:20 | history | bounty ended | Praphulla Koushik | ||
| S Jul 14, 2020 at 12:20 | history | notice removed | Praphulla Koushik | ||
| S Jul 13, 2020 at 4:56 | history | bounty started | Praphulla Koushik | ||
| S Jul 13, 2020 at 4:56 | history | notice added | Praphulla Koushik | Draw attention | |
| Jul 12, 2020 at 2:06 | answer | added | Dmitri Pavlov | timeline score: 6 | |
| Jul 10, 2020 at 18:07 | review | Close votes | |||
| Jul 10, 2020 at 19:42 | |||||
| Jul 10, 2020 at 16:56 | comment | added | Praphulla Koushik | @PhilTosteson Ok. I am afraid I might lost the path if I google for infinity topoi and look for relation with Piotr Achinger's comment. Can you suggest some starting point towards this? | |
| Jul 10, 2020 at 16:44 | comment | added | Phil Tosteson | I don't know a particularly good introduction because, like many of the core concepts that motivate infinity categories, this idea is folklore which only (relatively) recently accquired a more precise accepted meaning. But the point is that there is an infinity category of chain complexes $Ch$, and the functor $U \mapsto C^*(U)$ becomes a sheaf in the infinity categorical sense. (In turn $\infty$-categories of sheaves of spaces (instead of chain complexes) are the paradigmatic example of $\infty$-topoi). | |
| Jul 10, 2020 at 16:08 | history | edited | Praphulla Koushik | CC BY-SA 4.0 |
added 195 characters in body
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| Jul 9, 2020 at 18:19 | comment | added | Praphulla Koushik | This upvote downvote game is funny :D 3 upvotes, 2 downvotes. | |
| Jul 9, 2020 at 18:03 | comment | added | Praphulla Koushik | @PiotrAchinger that is interesting. can you please suggest some (possibly short) reference that introduce $\infty$-topoi when trying to understand in what sense cohomology is a sheaf? | |
| Jul 9, 2020 at 18:01 | comment | added | Piotr Achinger | The question is not stupid - trying to make sense of "in what way is cohomology a sheaf" leads one to notions like $\infty$-topoi etc. | |
| Jul 9, 2020 at 17:58 | comment | added | Praphulla Koushik | @PiotrAchinger Ok. It is not immediate for me, I will think about it. Thanks :) | |
| Jul 9, 2020 at 17:55 | comment | added | Praphulla Koushik | Oh, no. I did not think about that @MikeMiller. That is straight forward that it is not expected to be sheaf.. this is a stupid question. I should not have asked it here (not in this form) :D | |
| Jul 9, 2020 at 17:54 | comment | added | mme | No, as almost any example demonstrates (a sphere, for instance, covered by two contractible open sets); if cohomology were a sheaf the Mayer-Vietoris sequence would split as short exact sequences of $H^k$ for each $k$. $C^*(M)$ forms a sheaf of complexes, but the gluing property does not survive passing to cohomology. | |
| Jul 9, 2020 at 17:52 | comment | added | Piotr Achinger | No, in fact the cohomology presheaves $U\mapsto H^n_{\rm dR}(U)$ sheafify to zero for $n>0$. | |
| Jul 9, 2020 at 17:45 | history | asked | Praphulla Koushik | CC BY-SA 4.0 |