Lemma 101.10.2 (0CHV)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.10: Integral and finite morphisms
Lemma 101.10.2 (cite)

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Lemma 101.10.2. Let $\mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Let $\mathcal{Z} \to \mathcal{Y}$ be an integral (or finite) morphism of algebraic stacks. Then $\mathcal{Z} \times _\mathcal {Y} \mathcal{X} \to \mathcal{X}$ is an integral (or finite) morphism of algebraic stacks.

Proof. This follows from the discussion in Properties of Stacks, Section 100.3. $\square$

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