#
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

$h F_0 : h C_0 \to h D_0$

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 September 2, 2022 at 23:18:17.
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