The Stacks project

Lemma 106.8.2. A morphism $f : \mathcal{X} \to \mathcal{Y}$ of algebraic stacks is formally smooth (Definition 106.8.1) if and only if for every diagram (106.8.1.1) and $\gamma $ the category of dotted arrows is nonempty.

Proof. Translation between different languages omitted. $\square$

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