'In the category of sets, every monomorphism (injective function) with a non-empty domain is a section, and every epimorphism (surjective function) is a retraction; the latter statement is equivalent to the axiom of choice.' https://en.wikipedia.org/wiki/Section_(category_theory) Hence, Why surjective functions is retractive? Also why injective one = the axiom of choice?
Useful reading summary from Sections and Retractions http://theurbanengine.com/blog//sections-and-retractions