Section (Category Theory)

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

Remarks

A section that is also a retraction is an Isomorphism. A section that is also epic is also an Isomorphism. If $f$ has a section then $f$ is necessarily monic.