Implication Details
Claim: Given a functor whose codomain is epi-regular, if it preserves epimorphisms, then it preserves regular epimorphisms.
Proof: This follows from the dual implication.
Claim: Given a functor whose codomain is epi-regular, if it preserves epimorphisms, then it preserves regular epimorphisms.
Proof: This follows from the dual implication.