The Stacks project

Lemma 18.33.6. Let $\mathcal{C}$ be a site. Let $\varphi : \mathcal{O}_1 \to \mathcal{O}_2$ be a homomorphism of sheaves of rings. For any object $U$ of $\mathcal{C}$ there is a canonical isomorphism

\[ \Omega _{\mathcal{O}_2/\mathcal{O}_1}|_ U = \Omega _{(\mathcal{O}_2|_ U)/(\mathcal{O}_1|_ U)} \]

compatible with universal derivations.

Proof. This is a special case of Lemma 18.33.5. $\square$

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