CatDat

Implication Details

Claim: If a morphism is a split monomorphism, then it is a regular monomorphism.

Proof: Let $f : A \to B$ be a split monomorphism, and choose a morphism $g : B \to A$ with $g \circ f = \id_A$. Then it is easy to check that $f$ is an equalizer of $\id_B, f \circ g : B \rightrightarrows B$.