Definition:Functor Category
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Definition
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.