nLab equivalence of (infinity,1)-categories

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.

Revised on April 16, 2015 07:23:10 by Urs Schreiber (195.113.30.252)