3 problems

Characterization conjecture. The infinity-topoi are exactly the Segal categories of simplicial presheaves on Grothendieck sites.

Giraud's theorem for Segal topoi. $A$ is a $\mathbb{U}$-Segal topos if and only if:

A $(\infty,1)$-topos is a higher-categorical generalisation of a topos, and homotopy type theory is a type-theoretic framework with an univalence axiom and related rules for descri…