The Stacks project

Definition 83.6.1. 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 coarse quotient if

1. $\phi $ is a categorical quotient, and

2. $\phi $ is an orbit space.

If $S = B$, $U$, $R$ are all schemes, then we say a morphism of schemes $\phi : U \to X$ is a coarse quotient in schemes if

1. $\phi $ is a categorical quotient in schemes, and

2. $\phi $ is an orbit space.