Definition 39.3.3. Let $S$ be a scheme. Let $U$ be a scheme over $S$. Let $j : R \to U \times _ S U$ be a pre-relation. Let $g : U' \to U$ be a morphism of schemes. The pre-relation $j' : R' \to U' \times _ S U'$ is called the restriction, or pullback of the pre-relation $j$ to $U'$. In this situation we sometimes write $R' = R|_{U'}$.

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