Definition 81.10.1. Let $S$ be a scheme and $B$ an algebraic space over $S$. Let $j : R \to U \times _ B U$ be a pre-relation. A morphism $\phi : U \to X$ of algebraic spaces over $B$ is called a geometric quotient if
$\phi $ is an orbit space,
condition (1) holds universally, i.e., $\phi $ is universally submersive, and
the functions on $X$ are the $R$-invariant functions on $U$.