Lemma 4.8.3. Let $\mathcal{C}$ be a category. Let $a : F \to G$ be a morphism of contravariant functors from $\mathcal{C}$ to $\textit{Sets}$. If $a$ is representable, and $G$ is a representable functor, then $F$ is representable.

Proof. Omitted. $\square$

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