The Stacks project

Definition 94.19.2. Let $\mathit{Sch}_{fppf}$ be a big fppf site. Let $S \to S'$ be a morphism of this site. If $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ is an algebraic stack over $S$, then $\mathcal{X}$ viewed as an algebraic stack over $S'$ is the algebraic stack

\[ \mathcal{X} \longrightarrow (\mathit{Sch}/S')_{fppf} \]

gotten by applying construction A of Lemma 94.19.1 to $\mathcal{X}$.

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