The Stacks project

Lemma 10.132.1. Suppose that we have ring maps $A \to A'$ and $A \to B$. Set $B' = B \otimes _ A A'$, so that we obtain a diagram as above. Then the canonical map defined above induces an isomorphism $\Omega ^\bullet _{B/A} \otimes _ A A' = \Omega ^\bullet _{B'/A'}$ of complexes.

Proof. This follows from Lemma 10.131.12 and the fact that taking exterior powers commutes with base change. $\square$

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