Timeline for Subcategory of coherent objects in an $\infty$-topos forming a local $\infty$-pretopos
Current License: CC BY-SA 4.0
4 events
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| Mar 22, 2022 at 7:12 | comment | added | Marc Hoyois | Yeah I guess so. You can just replace a general topos by the slice topos over the geometric realization, then apply A.5.5.1 as stated. | |
| Mar 21, 2022 at 17:36 | comment | added | Markus Zetto | Thanks a lot, that is certainly easier than I thought it was going to be! Could one also use this argument in the proof of Theorem A.5.5.1, which states that in a locally $n$-coherent $\infty$-topos, the geometric realization of a semisimplicial object that is "pointwise" coherent and satisfies the Kan condition is still coherent? At the end of it, A.2.1.2 is used in a very similar way it is used here, so a similar argument might be able to completely get rid of the assumtion that $\mathcal{X}$ is locally $n$-coherent (note there's again an effective epimorphism from $X_0$ to $|X_\bullet|$) | |
| Mar 21, 2022 at 11:38 | vote | accept | Markus Zetto | ||
| Mar 21, 2022 at 9:48 | history | answered | Marc Hoyois | CC BY-SA 4.0 |