[[Category theory MOC]]
# Representable functor

A [[functor]] $F : \cat C \to \Set$ is **representable** iff it is [[Natural isomorphism|naturally isomorphic]] to the fixed-domain [[Hom-functor]] $h_{C} = \cat C(C,-)$ for some object $C \in \cat C$ #m/def/cat 
$$
\begin{align*}
\eta: h_{C} \Rightarrow F : \cat C \to \Set
\end{align*}
$$
whence $(C,\eta)$ is called a **representation** of $F$. 

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