Timeline for What is a morphism of ∞-sites?
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| Mar 21, 2020 at 11:56 | comment | added | Dylan Wilson | @DmitriPavlov that's why I said it might not be the generality you want. but not all pullbacks are assumed, only pullbacks along covers. so the site of smooth manifolds is okay here, right? anyway, I agree the theory in that appendix is probably not quite what you want, and only mention it because I thought it may still be helpful. | |
| Mar 21, 2020 at 1:32 | comment | added | Dmitri Pavlov | @DylanWilson: Definition A.10 of morphisms of ∞-sites in this paper assumes the existence of pullbacks, i.e., finite ∞-limits. Also, Proposition A.13 constructs geometric morphisms of ∞-toposes under a rather strong additional assumption of a covering lifting property. | |
| Mar 21, 2020 at 1:12 | comment | added | Dylan Wilson | the appendix of this paper develops some of this theory (but maybe not in the generality you wanted?): arxiv.org/abs/1803.01804 | |
| Mar 21, 2020 at 0:49 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
added 20 characters in body
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| Mar 21, 2020 at 0:48 | comment | added | Dmitri Pavlov | @SimonHenry: The toposes in this question are not hypercompleted, although an answer in the hypercompleted case would also be interesting. | |
| Mar 21, 2020 at 0:39 | comment | added | Simon Henry | I havn't really thought about it, but you might get two different answer depending if you use site to represente hypercomplete $\infty$-topos or topological localization of presheaves categories... | |
| Mar 20, 2020 at 22:19 | history | asked | Dmitri Pavlov | CC BY-SA 4.0 |