functor category

Let \(\mathcal{C}, \mathcal{D}\) be categories. then the functor category \(\mathcal{D}^{\mathcal{C}}\) is defined as category containing

1. functors \(\mathcal{F}: \mathcal{C} \rightarrow \mathcal{D}\) as objects
2. natural transformations as morphisms

• identity natural transformation
• composition of natural transformations as natural transformation