nLab
essentially surjective (infinity,1)-functor

Contents

Definition

An (,1)(\infty,1)-functor F:CDF : C \to D is essentially surjective if, when modeled as a functor of simplicially enriched categories, the induced functor

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

of ordinary categories 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.

Revised on May 11, 2012 11:59:47 by Urs Schreiber (82.169.65.155)