The Stacks project

Definition 101.39.6. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. We say $f$ satisfies the uniqueness part of the valuative criterion if for every diagram (101.39.1.1) and $\gamma$ as in Definition 101.39.1 the category of dotted arrows is either empty or a setoid with exactly one isomorphism class.