The Stacks project

Lemma 65.3.2. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. Let $F, G, H : (\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}$. Let $a : F \to G$, $b : G \to H$ be representable transformations of functors. Then

\[ b \circ a : F \longrightarrow H \]

is a representable transformation of functors.

Proof. This is entirely formal and works in any category. $\square$

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