Timeline for A hypercover of profinite sets as a limit of hypercovers of finite sets
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 25, 2023 at 12:01 | comment | added | Peter Scholze | Whoops, you are right. (For the application, it only matters to have this limit property on semi-simplicial sets, and that each term admits some refinement to have a simplicial set.) But you can correct this by approximating also the degeneracies mapping towards $T_n$ (so $T_n$ and all $T_{n,i}$ come sandwiched between two given things). | |
| Oct 24, 2023 at 1:31 | comment | added | gdb | >But for higher 𝑛, one is in the similar situation ... Dear Peter, could you clarify, please, how to construct the degeneracy maps in this inductive procedure? Unless I miss something, the argument seems to explain only how to get the face maps. Of course, for each particular i, the map $T_{n, i} \to (\mathrm{cosk}_{n-1} T_{\leq n-1, i})_n$ admits a section, so one can define degeneracy maps using this section. But it is not clear why it is possible to do compatibly for all $i$ (and it is probably false that these deg. maps are compatible with the degeneracy maps of $T_\bullet$) | |
| Nov 25, 2022 at 14:29 | vote | accept | Michael Barz | ||
| Nov 25, 2022 at 9:52 | history | answered | Peter Scholze | CC BY-SA 4.0 |