Definition:Functor Category

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Let $C$ and $D$ be categories.

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

Objects:         covariant functors $C \to D$
Morphisms: natural transformations
Composition: vertical composition of natural transformations
Identity morphisms: identity natural transformations

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