Definition:Functor Category

Definition
Let $C$ and $D$ be categories.

The functor category $\operatorname{Funct}(C, D)$ is the category with:

Also denoted as
The functor category is also denoted $\operatorname{Fun}(C, D)$, $[C, D]$ or $D^C$, in analogy to the set of all mappings.

Also see

 * Functor Category is Category