Lemma 101.45.1 (0DU7)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 101: Morphisms of Algebraic Stacks
Section 101.45: Stabilizer preserving morphisms
Lemma 101.45.1 (cite)

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Lemma 101.45.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. If $\mathcal{I}_\mathcal {X} \to \mathcal{X} \times _\mathcal {Y} \mathcal{I}_\mathcal {Y}$ is an isomorphism, then $f$ is representable by algebraic spaces.

Proof. Immediate from Lemma 101.6.2. $\square$

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