Timeline for Examples of $(\infty,1)$-topoi that are not given as sheaves on a Grothendieck topology
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4, 2017 at 6:44 | comment | added | David Corfield | Of related interest, just as Grothendieck toposes were generalized to elementary toposes, Mike Shulman has proposed a notion of elementary ∞-toposes here golem.ph.utexas.edu/category/2017/04/elementary_1topoi.html, written up as this nLab entry ncatlab.org/nlab/show/elementary+%28infinity%2C1%29-topos. | |
| Jun 27, 2017 at 8:53 | vote | accept | Georg Lehner | ||
| Jun 27, 2017 at 4:56 | answer | added | Jacob Lurie | timeline score: 20 | |
| Jun 27, 2017 at 3:17 | comment | added | Marc Hoyois | They are useful to have! There are many natural examples of ∞-topoi that have a priori nothing to do with Grothendieck topologies, such as ∞-categories of n-excisive or finitary functors with values in an ∞-topos, or ∞-categories of coalgebras in an ∞-topos. These may happen to be ∞-category of sheaves "by accident", and I don't know how one could rule that out, but knowing they are sheaves would not be useful. | |
| Jun 26, 2017 at 21:14 | history | asked | Georg Lehner | CC BY-SA 3.0 |