nLab essentially surjective (infinity,1)-functor

Context

$(\infty,1)$-Category theory

(∞,1)-category theory

Contents

Definition

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

$h F_0 : h C_0 \to h D_0$

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.

Revised on May 11, 2012 11:59:47 by Urs Schreiber (82.169.65.155)