Lemma 35.3.3. Let $R \to A$ be a ring map. Let $M$ be an $R$-module. The cosimplicial $(A/R)_\bullet $-module associated to the canonical descent datum is isomorphic to the cosimplicial module $(A/R)_\bullet \otimes _ R M$.

**Proof.**
Omitted.
$\square$

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