nLab essentially surjective (infinity,1)-functor

Contents

Contents

Definition

An (,1)(\infty,1)-functor F:CDF : C \to D is essentially surjective if the induced functor of the core infinity-groupoids

core(F 0):core(C 0)core(D 0) core(F_0) : core(C_0) \to core(D_0)

is an effective epimorphism.

An (,1)(\infty,1)-functor F:CDF : C \to D is essentially surjective if the induced functor of the homotopy categories of the (,1)(\infty,1)-categories

hF 0:hC 0hD 0 h F_0 : h C_0 \to h D_0

is essentially surjective

Properties

An (∞,1)-functor which is both essentially surjective as well as full and faithful (∞,1)-functor is precisely an equivalence of (∞,1)-categories.

basic properties of…

Last revised on September 2, 2022 at 19:18:17. See the history of this page for a list of all contributions to it.