The Stacks project

Remark 90.23.2. We note that this terminology is potentially confusing: if $(U, R, s, t, c)$ is a smooth groupoid in functors, then the quotient $[U/R]$ need not be a smooth category cofibred in groupoids as defined in Definition 90.9.1. However smoothness of $(U, R, s, t, c)$ does imply (in fact is equivalent to) smoothness of the quotient morphism $U \to [U/R]$ as we shall see in Lemma 90.23.4.

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