Let $f:A \to B$ be a function of sets. If $f$ has a section, $s:B\to A$, satisfying by definition $f\circ s=\text{id}_B$, then it is straightforward to show that $f$ is an epimorphism (i.e. surjective). My question is simple, is the opposite true?
Given an epimorphism $f:A\to B$, does there exists a section for it?