# nLab essentially surjective (infinity,1)-functor

### Context

#### $\left(\infty ,1\right)$-Category theory

(∞,1)-category theory

# Contents

## Definition

An $\left(\infty ,1\right)$-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.

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