[[Category theory MOC]]
# Functor category

Given two categories $\cat C$ and $\cat D$, we construct a **functor category** $\cat D^{\cat C}$ where each object is a functor and
each morphism is a [[natural transformation]] $\eta : F \Rightarrow G : \cat C \to \cat D$.

## Special cases

- [[Endofunctor category]] $\cat C^\cat{C}$, which possesses additional monoidal structure.
- [[Category of presheaves]] $\Set^{\op{\cat C}}$

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