The Stacks project

Lemma 101.37.4. A closed immersion of algebraic stacks is a proper morphism of algebraic stacks.

Proof. A closed immersion is by definition representable (Properties of Stacks, Definition 100.9.1). Hence this follows from the discussion in Properties of Stacks, Section 100.3 and the corresponding result for morphisms of algebraic spaces, see Morphisms of Spaces, Lemma 67.40.5. $\square$

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