Timeline for unbounded derived category of a $\infty$-topos
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2023 at 14:48 | answer | added | Bingyu Zhang | timeline score: 1 | |
| Dec 7, 2014 at 20:33 | comment | added | Marc Hoyois | Hypercompleteness is defined in HTT 6.5.2. The point is that $Shv^{hyp}(X)$ is the localization of $Shv(X)$ at morphisms which induce isomorphisms on homotopy groups. From this it's easy to show that $Shv^{hyp}(X,\mathfrak{C})$ is the localization of $Shv(X,\mathfrak{C})$ at the quasi-isomorphisms. | |
| Dec 7, 2014 at 15:21 | vote | accept | user55871 | ||
| Dec 7, 2014 at 5:18 | history | edited | user55871 | CC BY-SA 3.0 |
added 582 characters in body
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| Dec 6, 2014 at 16:11 | comment | added | Dylan Wilson | On the other hand, I think the two may agree if the $\infty$-topos is hypercomplete. | |
| Dec 6, 2014 at 16:05 | comment | added | Dylan Wilson | Lurie does not claim (and I think it might be false) that you get Spaltenstein's unbounded derived category this way. In fact, I think the whole point is that you do not, since base change fails for Spaltenstein's category. Maybe the two agree under some conditions. In any case, you do get a copy of bounded below derived category living inside. | |
| Dec 6, 2014 at 15:53 | answer | added | prefaisceau | timeline score: 10 | |
| Dec 6, 2014 at 14:23 | review | First posts | |||
| Dec 6, 2014 at 14:47 | |||||
| Dec 6, 2014 at 14:22 | history | asked | user55871 | CC BY-SA 3.0 |