Lemma 64.5.5. 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. Let $a : F \to G$ be a representable transformations of functors. Let $b : H \to G$ be any transformation of functors. Consider the fibre product diagram

If $a$ has property $\mathcal{P}$ then also the base change $a'$ has property $\mathcal{P}$.

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