Implication details

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

Proof: Let

m : A \to B

be a split monomorphism, and choose a morphism

e : B \to A

with

e \circ m = \id_A

. Then it is easy to check that

m

is an equalizer of

\id_B

and the idempotent morphism

m \circ e : B \to B

.

This implication has a dual.

Show 6 morphisms using this implication