nLab
epimorphism in an (infinity,1)-category

Contents

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

Last revised on May 14, 2018 at 05:44:06. See the history of this page for a list of all contributions to it.