The Stacks project

Remark 90.9.2. Suppose $\mathcal{F}$ is a predeformation category admitting a smooth morphism $\varphi : \mathcal U \to \mathcal{F}$ from a predeformation category $\mathcal{U}$. Then by Lemma 90.8.8 $\varphi $ is essentially surjective, so by Lemma 90.8.7 $p: \mathcal{F} \to \mathcal{C}_\Lambda $ is smooth if and only if the composition $\mathcal U \xrightarrow {\varphi } \mathcal{F} \xrightarrow {p} \mathcal{C}_\Lambda $ is smooth, i.e. $\mathcal{F}$ is smooth if and only if $\mathcal{U}$ is smooth.