The Stacks project

Definition 92.19.3. Let $\mathit{Sch}_{fppf}$ be a big fppf site. Let $S \to S'$ be a morphism of this site. Let $\mathcal{X}'$ be an algebraic stack over $S'$. The change of base of $\mathcal{X}'$ is the algebraic space $\mathcal{X}'_ S$ over $S$ described above.

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