equivalences in/of $(\infty,1)$-categories
An $(\infty,1)$-functor $F : C \to D$ is essentially surjective if, when modeled as a functor of simplicially enriched categories, the induced functor
of ordinary categories is essentially surjective
An (∞,1)-functor which is both essentially surjective as well as full and faithful (∞,1)-functor is precisely an equivalence of (∞,1)-categories.