# Definition:Functor Category

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## Definition

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 |

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## 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

## Sources

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