The Stacks project

Lemma 94.6.3. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. Let $\mathcal{X}, \mathcal{Y}, \mathcal{Z}$ be categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$ Let $f : \mathcal{X} \to \mathcal{Y}$, $g : \mathcal{Y} \to \mathcal{Z}$ be representable $1$-morphisms. Then

\[ g \circ f : \mathcal{X} \longrightarrow \mathcal{Z} \]

is a representable $1$-morphism.

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

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