Rather little is known about the very general notion of higher topos theory. A rich theory however exists in the context of (∞,1)-categories, as described in Jacob Lurie's book Higher Topos Theory, which only covers the $(\infty, 1)$ case.

Just as the archetypical example of an ordinary topos (i.e. a $(1,1)$-topos) is Set – the category of 0-categories – so the $\infty$-category of n-categories or at least of $n$-groupoids should form the archetypical example of an $(n+1,1)$-topos.