# nLab equivalence of (infinity,1)-categories

Contents

### Context

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

(∞,1)-category theory

# Contents

## Definition

An (∞,1)-functor between (∞,1)-categories is an equivalence in (∞,1)Cat precisely if it is an essentially surjective (∞,1)-functor and a full and faithful (∞,1)-functor.

When (∞,1)-categories are presented by quasi-categories, an equivalence between them is presented by a weak equivalence in the model structure for quasi-categories.

## Properties

###### Lemma

An (∞,1)-functor $f : C \to D$ is an equivalence in (∞,1)Cat if the following equivalent conditions hold

###### Proof

This is HTT, lemma 3.1.3.2.

Last revised on April 16, 2015 at 07:23:10. See the history of this page for a list of all contributions to it.