Rather little is known about the very general notion of higher topos theory. A rich theory however exists in the context of (∞,1)-categories, see at (∞,1)-topos theory

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,r)-categories should form the archetypical example of an $(n+1,r+1)$-topos: