Implication Details
Claim: Given a morphism whose category is balanced, if it is an epimorphism and is a monomorphism, then it is an isomorphism.
Proof: This holds by definition of a balanced category.
Claim: Given a morphism whose category is balanced, if it is an epimorphism and is a monomorphism, then it is an isomorphism.
Proof: This holds by definition of a balanced category.