Timeline for Is there a condensed / pyknotic refinement of the shape of an $\infty$-topos?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2021 at 20:05 | vote | accept | Tim Campion | ||
| Feb 8, 2021 at 16:27 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Feb 8, 2021 at 16:26 | comment | added | Tim Campion | @PiotrAchinger Good question. Clearly I haven't considered this carefully, but it's already a bit of a lie to say that we're working with pro-discrete spaces, since unlike in the profinite case, the "take the limit" functor $Pro(Set) \to Top$ is not full (e.g. a pro-system of infinite sets can have empty limit without being pro-isomorphic to the empty set). So the future work of Barwick, Glasman, and Haine addressing this conjecture has a few conceptual stumbling blocks to work out! | |
| Feb 8, 2021 at 13:11 | vote | accept | Tim Campion | ||
| Feb 8, 2021 at 16:32 | |||||
| Feb 8, 2021 at 10:46 | answer | added | M L | timeline score: 9 | |
| Feb 8, 2021 at 8:12 | comment | added | Piotr Achinger | Side question: the etale homotopy type (Artin-Mazur) recovers the SGA3 (pro-discrete) etale fundamental group, which is smaller than the pro-etale fundamental group (Bhatt-Scholze). Do we expect the refinement you seek to have the pro etale fundamental group as its $\pi_1$? It’s not always pro-discrete as a group, only as a topological space (more precisely, a Noohi group). | |
| Feb 8, 2021 at 1:37 | history | edited | Tim Campion | CC BY-SA 4.0 |
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| Feb 8, 2021 at 1:29 | history | asked | Tim Campion | CC BY-SA 4.0 |