Timeline for classifying $\infty$-toposes for topological/localic groups?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2014 at 23:14 | vote | accept | Simon Henry | ||
| Jan 25, 2014 at 16:59 | answer | added | Jacob Lurie | timeline score: 10 | |
| Jan 22, 2014 at 6:42 | comment | added | Simon Henry | I agree with you, but for topological group which are not pro discrete (a compact connected topological group for instance) there is no classifying $1$-topos. Moreover, I don't see any reason why an infinity topos $\mathcal{T}$ such that for any localic topos $\mathcal{L}$ the category of morphisms from $\mathcal{L}$ to $\mathcal{T}$ is equivalent to a $1$-category should be a $1$-topos. Hence it is not impossible that for some topological group $G$ there is classifying infinity topos $BG$ which is not a $1$-topos. | |
| Jan 22, 2014 at 1:18 | comment | added | Anton Fetisov | If I understand correctly, you are only interested in localic topoi and G-bundles which are locales. If you are using "locale" in a common sense (a Heyting algebra), then I don't see why should you care about $\infty$-topoi. Your question seems to be purely 1-categorical, and is classical as such. | |
| Jan 21, 2014 at 21:03 | answer | added | Christopher Townsend | timeline score: 4 | |
| Jan 21, 2014 at 12:51 | answer | added | Marty | timeline score: 0 | |
| Jan 20, 2014 at 13:25 | history | edited | Simon Henry | CC BY-SA 3.0 |
edited title
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| Jan 20, 2014 at 13:12 | history | asked | Simon Henry | CC BY-SA 3.0 |