Lemma 100.9.2 (0501)—The Stacks project

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Part 7: Algebraic Stacks
Chapter 100: Properties of Algebraic Stacks
Section 100.9: Immersions of algebraic stacks
Lemma 100.9.2 (cite)

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Lemma 100.9.2. Let $\mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Let $\mathcal{Z} \to \mathcal{Y}$ be a (closed, resp. open) immersion. Then $\mathcal{Z} \times _\mathcal {Y} \mathcal{X} \to \mathcal{X}$ is a (closed, resp. open) immersion.

Proof. This follows from the general discussion in Section 100.3. $\square$

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