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.
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