# nLab essentially surjective (infinity,1)-functor

Contents

### Context

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

(∞,1)-category theory

Background

Basic concepts

Universal constructions

Local presentation

Theorems

Extra stuff, structure, properties

Models

# Contents

## Definition

An $(\infty,1)$-functor $F : C \to D$ is essentially surjective if the induced functor of the core infinity-groupoids

$core(F_0) : core(C_0) \to core(D_0)$

is an effective epimorphism.

An $(\infty,1)$-functor $F : C \to D$ is essentially surjective if the induced functor of the homotopy categories of the $(\infty,1)$-categories

$h F_0 : h C_0 \to h D_0$

## 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 September 2, 2022 at 19:18:17. See the history of this page for a list of all contributions to it.