Implication details
Claim: Given a morphism whose category is subobject-trivial, if it is a monomorphism, then it is an isomorphism.
Proof: This holds by definition of a subobject-trivial category.
This implication has a dual.
Claim: Given a morphism whose category is subobject-trivial, if it is a monomorphism, then it is an isomorphism.
This implication has a dual.