Representable functor

A functor $𝐹 : 𝖢 \to 𝖲 𝖾 𝗍$ is representable iff it is naturally isomorphic to the fixed-domain Hom-functor $ℎ 𝐶 = 𝖢 (𝐶, -)$ for some object $𝐶 \in 𝖢$ #m/def/cat

𝜂 : ℎ 𝐶 \Rightarrow 𝐹 : 𝖢 \to 𝖲 𝖾 𝗍

whence $(𝐶, 𝜂)$ is called a representation of $𝐹$ .

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