Lemma 76.15.11. Taking the universal first order thickenings commutes with étale localization. More precisely, let $h : Z \to X$ be a formally unramified morphism of algebraic spaces over a base scheme $S$. Let

be a commutative diagram with étale vertical arrows. Let $Z'$ be the universal first order thickening of $Z$ over $X$. Then $V \to U$ is formally unramified and the universal first order thickening $V'$ of $V$ over $U$ is étale over $Z'$. In particular, $\mathcal{C}_{Z/X}|_ V = \mathcal{C}_{V/U}$.

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