The Stacks project

Proof. Choose a scheme $U$ and a surjective étale morphism $U \to X$. Choose a scheme $V$ and a surjective étale morphism $V \to U \times _ X Y$. Choose a scheme $W$ and a surjective étale morphism $W \to V \times _ Y Z$. By Lemma 76.15.11 the morphisms $W \to V$ and $V \to U$ are formally unramified. Moreover the sequence $i^*\mathcal{C}_{Y/X} \to \mathcal{C}_{Z/X} \to \mathcal{C}_{Z/Y} \to 0$ restricts to the corresponding sequence $i^*\mathcal{C}_{V/U} \to \mathcal{C}_{W/U} \to \mathcal{C}_{W/V} \to 0$ for $W \to V \to U$. Hence the result follows from the result for schemes (More on Morphisms, Lemma 37.62.23) as by definition the morphism $W \to V$ is a local complete intersection morphism. $\square$