CatDat

Implication Details

Claim: Given a morphism whose category is balanced, if it is a monomorphism, then it is an extremal monomorphism.

Proof: Assume $m$ is a monomorphism that factors as $m = g \circ e$, where $e$ is an epimorphism. But then $e$ is also a monomorphism, and since the category is balanced, $e$ must be an isomorphism.