nLab
epimorphism in an (infinity,1)-category

Contents

Idea

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

Definition

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

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

is a monomorphism in an (∞,1)-category in ∞Grpd.

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