Definition 93.16.4. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $(U, R, s, t, c)$ be a groupoid in algebraic spaces over $B$. We say $(U, R, s, t, c)$ is a smooth groupoid1 if $s, t : R \to U$ are smooth morphisms of algebraic spaces.

[1] This terminology might be a bit confusing: it does not imply that $[U/R]$ is smooth over anything.

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