Lemma 100.43.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Assume $f$ is of finite type and quasi-separated. Then the following are equivalent

$f$ is proper, and

$f$ satisfies both the uniqueness and existence parts of the valuative criterion.

## Comments (4)

Comment #2971 by Daniel Loughran on

Comment #3096 by Johan on

Comment #5853 by Antoine Chambert-Loir on

Comment #5856 by Johan on