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