\begin{definition}[Definition:Functor Category]
Let $C$ and $D$ be categories.
The '''functor category''' $\operatorname{Funct}(C, D)$ is the category with:
{{DefineCategory
|ob = covariant functors $C \to D$
|mor = natural transformations
|comp = vertical composition of natural transformations
|id = identity natural transformations
}}
{{definition wanted|the contravariant case}}
\end{definition}