Let $\mathcal{C}$ be any category and let $A, B$ be objects. A retraction is a morphism $r: A\to B$ such that there is $s:B\to A$ such that $r\circ s:B\to B$ is the identity.
A morphism $l: A\to B$ is said to be left-factoring if for any $Z\in \mathbf{Ob}(\mathcal{C})$ and any morphism $f: Z\to B$ there is $h: Z\to A$ such that $f = l\circ h$. (I take this definition from Universal and left-factoring order-preserving maps.)
Is there any implication between these terms?