Lemma 100.45.1. 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 100.6.2.
$\square$

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