The Stacks project

Definition 78.4.3. Let $B \to S$ as in Section 78.3. Let $U$ be an algebraic space over $B$. Let $j : R \to U \times _ B U$ be a pre-relation. Let $g : U' \to U$ be a morphism of algebraic spaces over $B$. The pre-relation $j' : R' \to U' \times _ B U'$ of Lemma 78.4.2 is called the restriction, or pullback of the pre-relation $j$ to $U'$. In this situation we sometimes write $R' = R|_{U'}$.