Lemma 4.8.3 (03KC)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 4: Categories
Section 4.8: Fibre products and representability
Lemma 4.8.3 (cite)

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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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