nLab
essentially surjective (infinity,1)-functor

Definition

An $(\mathrm{\infty },1)$-functor $F:C\to D$ is essentially surjective if, when modeled as a functor of simplicially enriched categories, the induced functor

$$h{F}_0:h{C}_0\to h{D}_0$$h F_0 : h C_0 \to h D_0

of ordinary categories is essentially surjective

Properties

An (∞,1)-functor which is both essentially surjective as well as full and faithful (∞,1)-functor is precisely an equivalence of (∞,1)-categories.

Related concepts

• essentially surjective functor

• full and faithful (∞,1)-functor / fully faithful (infinity,1)-functor

• equivalence of (∞,1)-categories