Category of Functors

Given categories $\mathcal{C}$, $\mathcal{D}$, the category of Functor $[\mathcal{C},\mathcal{D}]$ is the category made up of:

• objects are functors $F:\mathcal{C}\Rightarrow \mathcal{D}$
• morphisms are natural transformations: $\mathcal{N}:F\Rightarrow G$

This satisfies the definition of a category.