Lemma 99.8.2. Let $\mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Let $\mathcal{Z} \to \mathcal{Y}$ be a monomorphism. Then $\mathcal{Z} \times _\mathcal {Y} \mathcal{X} \to \mathcal{X}$ is a monomorphism.

Proof. This follows from the general discussion in Section 99.3. $\square$

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