nLab
(eso+full, faithful) factorization system

Contents

Definition

In the 2-topos Cat, the pair of classes of morphisms (essentially surjective and full functors, faithful functors) form a factorization system in a 2-category. This factorization system can also be restricted to the (2,1)-topos Grpd.

In fact, an analogous factorization system exists in any 2-exact 2-category and any (2,1)-exact (2,1)-category, including any Grothendieck 2-topos or (2,1)-topos; see here.

Properties

More on this is at infinity-image – Of Functors between groupoids.

Revised on November 22, 2012 13:00:25 by Urs Schreiber (82.169.65.155)