nLab
epimorphism in an (infinity,1)-category

Contents

Idea

One analog in (∞,1)-category theory of epimorphism in category theory. Beware that there are other variants such as effective epimorphism in an (infinity,1)-category and generally the concept of n-epimorphism.

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.

Examples

Revised on February 25, 2015 15:29:44 by Urs Schreiber (195.113.30.252)