The Stacks project

Remark 22.13.7. Let $R$ be a ring. Let $A$ be a differential graded $R$-algebra. Let $M^\bullet $ and $N^\bullet $ be complexes of $R$-modules. Let $k \in \mathbf{Z}$ and consider the isomorphism

\[ \mathop{\mathrm{Hom}}\nolimits ^\bullet (M^\bullet , N^\bullet )[-k] \longrightarrow \mathop{\mathrm{Hom}}\nolimits ^\bullet (M^\bullet [k], N^\bullet ) \]

of complexes of $R$-modules defined in More on Algebra, Item (18). If $M^\bullet $ has the structure of a left, resp. right differential graded $A$-module, then this is a map of right, resp. left differential graded $A$-modules (with the module structures as defined in this section). We omit the verification; we warn the reader that the $A$-module structure on the shift of a left graded $A$-module is defined using a sign, see Definition 22.11.3.

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