Lemma 92.9.7. 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 $f : \mathcal{X} \to \mathcal{Y}$ be a $1$-morphism representable by algebraic spaces. Let $g : \mathcal{Z} \to \mathcal{Y}$ be any $1$-morphism. Consider the fibre product diagram

Then the base change $f'$ is a $1$-morphism representable by algebraic spaces.

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