The Stacks project

Remark 94.16.3. If the morphism $f : \mathcal{S}_ U \to \mathcal{X}$ of Lemma 94.16.2 is only assumed surjective, flat and locally of finite presentation, then it will still be the case that $f_{can} : [U/R] \to \mathcal{X}$ is an equivalence. In this case the morphisms $s$, $t$ will be flat and locally of finite presentation, but of course not smooth in general.