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 \colon X \to Y in 𝒞\mathcal{C} is an epimorphism if for all objects A𝒞A \in \mathcal{C} the induced morphism on hom \infty -groupoids

𝒞(f,A):𝒞(Y,A)𝒞(X,A) \mathcal{C}(f,A) \,\colon\, \mathcal{C}(Y,A) \xhookrightarrow{\;\;} \mathcal{C}(X,A)

is a monomorphism in ∞Grpd.

Examples

References

Last revised on November 22, 2021 at 03:03:28. See the history of this page for a list of all contributions to it.