Retraction (Category Theory)

Definition

In category theory a retraction of an arrow $f:a\to b$ is a left-inverse, $r:b\to a$ s.t. $r\circ f=\mathrm{id}$.

Remarks

A retraction that is also a section is an Isomorphism. A retraction that is also monic is also an Isomorphism. A retraction is necessarily epic.