Definition 63.16.2. Let $\mathit{Sch}_{fppf}$ be a big fppf site. Let $S \to S'$ be a morphism of this site.

If $F'$ is an algebraic space over $S'$, then the

*base change of $F'$ to $S$*is the algebraic space $j^{-1}F'$ described in Lemma 63.16.1. We denote it $F'_ S$.If $F$ is an algebraic space over $S$, then $F$

*viewed as an algebraic space over $S'$*is the algebraic space $j_!F$ over $S'$ described in Lemma 63.16.1. We often simply denote this $F$; if not then we will write $j_!F$.

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