The identity natural transformation $\text{id}_{F}\colon F\Longrightarrow F$ of $F$ is the natural transformation consisting of the collection
\[ \webleft\{ \text{id}_{F\webleft (A\webright )}\colon F\webleft (A\webright )\to F\webleft (A\webright )\webright\} _{A\in \text{Obj}\webleft (\mathcal{C}\webright )}. \]