A morphism is a universal epimorphism if for every morphism there is a pullback and its projection is an epimorphism.
In particular, setting , we see that itself is an epimorphism.
A morphism is a universal monomorphism if its opposite is a universal epimorphism in the opposite category. In particular, it is a monomorphism.
Revised on May 17, 2011 03:01:02
by Mike Shulman