Implication Details
Claim: If a category is epi-regular and is right cancellative, then it is subobject-trivial.
Proof: This is because a monomorphism which is also a regular epimorphism is an isomorphism.
Claim: If a category is epi-regular and is right cancellative, then it is subobject-trivial.
Proof: This is because a monomorphism which is also a regular epimorphism is an isomorphism.