Hello!
Is there a simple 'topological' condition to detect whenever a morphism of locale locales $f : X \rightarrow Y$ induce induces a surjection of infini topos infinity-toposes $f : Sh_{\infty}(X) \mathrm{Sh}_{\infty}(X) \rightarrow Sh_{\infty}(Y)$ \mathrm{Sh}_{\infty}(Y)$ (ie i.e. such that $f^*$ is conservative).?
It's not enough to assume that f is a Surjection surjection of local locales: indeed, if we take a topological space $X$ such that $Sh_{\infty}(X)$ \mathrm{Sh}_{\infty}(X)$ is not hypercomplete, and $X^{disc}$ his X^{\mathrm{disc}}$ is its space of points endowed with the discrete topology. Then , then $Sh_{\infty}(X^{disc}) \mathrm{Sh}_{\infty}(X^{\mathrm{disc}}) \rightarrow Sh_\infty \mathrm{Sh}_\infty (X)$ can't be a surjection, because the pull back pullback of an $\infty$-conected \infty$-connected map in $Sh_\infty \mathrm{Sh}_\infty (X)$are is a weak equivalence in $Sh_{\infty}(X^{disc})$..\mathrm{Sh}_{\infty}(X^{\mathrm{disc}})$...
Thank you!
