The Stacks project

Definition 106.8.1. A morphism $f : \mathcal{X} \to \mathcal{Y}$ of algebraic stacks is said to be formally smooth if it is formally smooth on objects as a $1$-morphism in categories fibred in groupoids as explained in Criteria for Representability, Section 97.6.

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View Definition 106.8.1 as pdf