Lemma 63.3.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$ and let $X$, $Y$ be objects of $(\mathit{Sch}/S)_{fppf}$. Let $f : X \to Y$ be a morphism of schemes. Then

is a representable transformation of functors.

Lemma 63.3.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$ and let $X$, $Y$ be objects of $(\mathit{Sch}/S)_{fppf}$. Let $f : X \to Y$ be a morphism of schemes. Then

\[ h_ f : h_ X \longrightarrow h_ Y \]

is a representable transformation of functors.

**Proof.**
This is formal and relies only on the fact that the category $(\mathit{Sch}/S)_{fppf}$ has fibre products.
$\square$

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