Are $\infty$-topoi determined by their localic points ? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T01:44:12Z http://mathoverflow.net/feeds/question/119557 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/119557/are-infty-topoi-determined-by-their-localic-points Are $\infty$-topoi determined by their localic points ? Simon Henry 2013-01-22T11:53:01Z 2013-01-25T05:26:29Z <p>Hello !</p> <p>If $T$ is an infinity topos, then you can consider the infinity category of geometric morphism from $Sh_{\infty}(\mathcal{L})$ to $T$ for any locale $\mathcal{L}$. This associate to $T$ an infinity stacks over the category of all locale (at least for the etale topology, but also probably for some stronger topology).</p> <p>My question is : is there anything know about this functor ? is it fully faithful ? or does it has some kind of "conservativity" properties that could allow to give an answer to the question in the tittle ? Or in the contrary is there example of non trivial infinity topos with no (or not enough) morphism from non trivial locale ?</p> <p>thank you !</p>