The Stacks project

Definition 78.17.2. Let $B \to S$ as in Section 78.3. Let $(U, R, s, t, c)$ be a groupoid in algebraic spaces over $B$. Let $g : U' \to U$ be a morphism of algebraic spaces over $B$. The morphism of groupoids in algebraic spaces $(U', R', s', t', c') \to (U, R, s, t, c)$ constructed in Lemma 78.17.1 is called the restriction of $(U, R, s, t, c)$ to $U'$. We sometime use the notation $R' = R|_{U'}$ in this case.