(∞,1)-category of (∞,1)-sheaves
(2,1)-quasitopos?
models for ?-stack (∞,1)-toposes?
structures in a cohesive (∞,1)-topos
fundamental ?-groupoid in a locally ?-connected (∞,1)-topos?/of a locally ?-connected (∞,1)-topos?
categorical/geometric homotopy groups
A separated (∞,1)-presheaf over an (∞,1)-site $C$ is a (∞,1)-presheaf $X : C^{op} \to$ ?Grpd? such that covering families $\{U_i \to U\}$ in $C$ the descent comparison morphism
is a full and faithful (∞,1)-functor and hence exhibits a full sub-(∞,1)-category.
(Here $S(\{U_i\})$ denotes the sieve associated to the cover).
More generally, $X$ is $k$-separated for $k \in \mathbb{N}$ if the descent morphism is a $(k-2)$-truncated morphism.
Notice that this means that a 0-separated $(\infty,1)$-presheaf is one whose descent morphisms are equivalences, hence those which are (∞,1)-sheaves.
separated (∞,1)-presheaf