identity natural transformation

Let \(\mathcal{C}, \mathcal{D}\) be categories and \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) a functor. Then the identity natural transformation is defined as

\begin{align*} \mathrm{id}_{\mathcal{F}}: \mathcal{F} \Rightarrow& \mathcal{F} \\ A \mapsto& \mathrm{id}_{\mathcal{F}(A)} \end{align*}