idempotent morphism

Let \(\mathcal{C}\) be a category, \(A \in \mathrm{Ob}(\mathcal{C})\) an object and \(f \in \mathrm{Hom}_{\mathcal{C}}(A,A)\) a morphism. then \(f\) is said to be idempotent, if

\begin{align*} f \circ f = f \end{align*}