Lemma 101.9.2. Let $\mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Let $\mathcal{Z} \to \mathcal{Y}$ be an affine morphism of algebraic stacks. Then $\mathcal{Z} \times _\mathcal {Y} \mathcal{X} \to \mathcal{X}$ is an affine morphism of algebraic stacks.
Proof. This follows from the discussion in Properties of Stacks, Section 100.3. $\square$
Comments (0)