nLab
universal epimorphism

A morphism f:XY is a universal epimorphism if for every morphism u:VY there is a pullback X× YV and its projection u *(f):X× YVV is an epimorphism.

In particular, setting u=id Y:YY, we see that f itself is an epimorphism.

A morphism g:XY is a universal monomorphism if its opposite g :Y X 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 (71.136.238.9)