Definition 24.25.2. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $(\mathcal{A}, \text{d})$ be a sheaf of differential graded algebras on $(\mathcal{C}, \mathcal{O})$. A diffential graded $\mathcal{A}$-module $\mathcal{I}$ is said to be graded injective1 if $\mathcal{M}$ viewed as a graded $\mathcal{A}$-module is an injective object of the category $\textit{Mod}(\mathcal{A})$ of graded $\mathcal{A}$-modules.

[1] This may be nonstandard terminology.

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