functor preserving pushouts preserves epimorphisms
1. Proposition
Let be categories,
be a functor preserving pushouts.
Then
preserves epimorphisms
2. Proof
Suppose is an epimorphism.
Then by epimorphism and pushout
is a pushout.
Since preserves pushouts, we get
Thus again by epimorphism and pushout, is an epimorphism.