Lemma 17.29.2. Let $f : Y \to X$ be a continuous map of topological spaces. Let $\mathcal{A} \to \mathcal{B}$ be a homomorphism of sheaves of rings on $X$. Then there is a canonical identification $f^{-1}\Omega ^\bullet _{\mathcal{B}/\mathcal{A}} = \Omega ^\bullet _{f^{-1}\mathcal{B}/f^{-1}\mathcal{A}}$ of de Rham complexes.

Proof. Omitted. Hint: compare with Lemma 17.27.6. $\square$

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