Lemma 64.5.4. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. Let $F, G, H : (\mathit{Sch}/S)_{fppf}^{opp} \to \textit{Sets}$. Let $\mathcal{P}$ be a property as in Definition 64.5.1 which is stable under composition. Let $a : F \to G$, $b : G \to H$ be representable transformations of functors. If $a$ and $b$ have property $\mathcal{P}$ so does $b \circ a : F \longrightarrow H$.

**Proof.**
Note that the lemma makes sense by Lemma 64.3.2. Proof omitted.
$\square$

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