The Stacks project

Example 107.5.15. If $\mathcal{X}$ is locally of finite type over a universally catenary locally Noetherian scheme $S$, and $U\to \mathcal{X}$ is a smooth surjective morphism whose source is a scheme, then the composite $U \to \mathcal{X} \to S$ is locally of finite type, and so $U$ is universally catenary Morphisms, Lemma 29.17.2. Thus $\mathcal{X}$ is pseudo-catenary.