Definition:Representation of Functor
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Definition
Let $\mathbf C$ be a locally small category.
Let $\mathbf{Set}$ be the category of sets.
Let $F : \mathbf C \to \mathbf{Set}$ be a covariant functor.
A representation of $F$ is a pair $\tuple {C, \eta}$ where $\eta : \map {\operatorname {Hom} } {C, \cdot} \to F$ is a natural isomorphism with the covariant hom functor of $C$.
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