split mono

Let \(\mathcal{C}\) be a category and \(f \in \mathrm{Hom}_{\mathcal{C}}(A,B)\). Then \(f\) is said to be a spilt mono, if there exists a left-inverse \(g \in \mathrm{Hom}_{\mathcal{C}}(B,A)\) such that

\begin{align*} g \circ f = \mathrm{id}_{A} \end{align*}