nLab infinity-topos

A notion of $\infty$-topos is a generalization of that of topos to higher category theory.

If by $\infty$-category one means an $(\infty,\infty)$-category, then such a notion is still undefined. However, nowadays many people write “$\infty$-category” to mean what here on the nLab we usually still call an (∞,1)-category, and thus an “$\infty$-topos” means an (∞,1)-topos. See also higher topos theory for more.