\begin{definition}[Definition:Identity Functor]
Let $\mathbf C$ be a metacategory.
The '''identity functor on $\mathbf C$''' is the functor $\operatorname{id}_{\mathbf C}: \mathbf C \to \mathbf C$ defined by:
:For all objects $C$ of $\mathbf C$: $\hskip{2.9cm} \operatorname{id}_{\mathbf C} C := C$
:For all morphisms $f: C_1 \to C_2$ of $\mathbf C$: $\quad \operatorname{id}_{\mathbf C} f := f$
That $\operatorname{id}_{\mathbf C}$ constitutes a functor is shown on Identity Functor is Functor.
\end{definition}