# nLab epimorphism in an (infinity,1)-category

### Context

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

(∞,1)-category theory

# Contents

## Idea

The analog in (∞,1)-category theory of epimorphism in category theory.

## Definition

For $C$ an (∞,1)-category, a morphism $f : X \to Y$ in $C$ is an epimorphism if for all $A \in C$ the induced morphism

$C(f,A) : C(Y,A) \to C(X,A)$

Created on October 18, 2010 23:04:59 by Urs Schreiber (131.211.232.170)