The Stacks project

Definition 78.19.3. In the situation of Definition 78.19.1. We say that the pre-relation $j$ has a quotient representable by an algebraic space if the sheaf $U/R$ is an algebraic space. We say that the pre-relation $j$ has a representable quotient if the sheaf $U/R$ is representable by a scheme. We will say a groupoid in algebraic spaces $(U, R, s, t, c)$ over $B$ has a representable quotient (resp. quotient representable by an algebraic space) if the quotient $U/R$ with $j = (t, s)$ is representable (resp. an algebraic space).