Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
have created an entry homotopy dimension
I have spelled out at homotopy dimension the proof that the $\infty$-presheaf topos on a site with terminal object has homotopy dimension $\leq 0$. And I have made explicit that the argument straightforwardly generalizes to imply that every local (infinity,1)-topos has homotopy dimension $\leq 0$.
This implies a whole chain of immediate pleasant results:
every local $\infty$-topos is
of cohomology dimension $\leq 0$
and hypercomplete;
hence
every cohesive (infinity,1)-topos is
of cohomology dimension $\leq 0$
and hypercomplete.
1 to 2 of 2