Implication details
Claim: Given a morphism whose category is regular, if it is an extremal epimorphism, then it is a regular epimorphism.
Proof: This follows from the dual implication.
This implication has a dual.
Claim: Given a morphism whose category is regular, if it is an extremal epimorphism, then it is a regular epimorphism.
This implication has a dual.