The Stacks project

Definition 78.19.1. Let $B \to S$ and the pre-relation $j : R \to U \times _ B U$ be as above. In this setting the quotient sheaf $U/R$ associated to $j$ is the sheafification of the presheaf (78.19.0.1) on $(\mathit{Sch}/S)_{fppf}$. If $j : R \to U \times _ B U$ comes from the action of a group algebraic space $G$ over $B$ on $U$ as in Lemma 78.15.1 then we denote the quotient sheaf $U/G$.