normal monomorphism

Let \(\mathcal{C}\) be a category and \(f \in \mathrm{Hom}_{\mathcal{C}}(A,B)\) a monomorphism for objects \(A,B \in \mathrm{Ob}(\mathcal{C})\). Then \(f\) is said to be normal, if there exists an object \(C \in \mathrm{Ob}(\mathcal{C})\) and a morphism \(g \in \mathrm{Hom}_{\mathcal{C}}(B,C)\), such that \(f: A \rightarrow B\) is isomorphic to the kernel \(\mathrm{ker}(g)\).