Lemma 101.38.4. Let
be a commutative diagram of algebraic stacks. Let \mathcal{Z}_ i \subset \mathcal{Y}_ i, i = 1, 2 be the scheme theoretic image of f_ i. Then the morphism \mathcal{Y}_1 \to \mathcal{Y}_2 induces a morphism \mathcal{Z}_1 \to \mathcal{Z}_2 and a commutative diagram
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