I am trying to prove that in an Abelian Category, the morphism $(\pi_A, \pi_B): A \sqcup B \rightarrow A \times B$ is an isomorphism so that finite Products and Coproducts coincide.
I know the proofs for Monomorphism and Epimorphism are going to be similar so I wanted to see if given the proof for Epic, I can figure out proof for Monic.
Edit: I have to prove by hand that this map is Epic