# 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.

Last revised on May 11, 2012 at 11:59:47. See the history of this page for a list of all contributions to it.