split epi

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

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