Lemma 22.13.3. In the situation above, let $A$ be a differential graded $R$-algebra. To give a right $A$-module structure on $M$ is the same thing as giving a homomorphism $\tau : A \to E^{opp}$ of differential graded $R$-algebras.

**Proof.**
See discussion above and note that the construction of $\tau $ from the multiplication map $M^ n \times A^ m \to M^{n + m}$ uses signs.
$\square$

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