Definition:Functor Category

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Let $C$ and $D$ be categories.

The functor category $\map {\operatorname{Funct} } {C, D}$ 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 van also be denoted $\map {\operatorname{Fun} } {C, D}$, $\sqbrk {C, D}$ or $D^C$, in analogy to the set of all mappings.

Also see