The Stacks project

Definition 24.21.2. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{A}$ be a sheaf of differential graded algebras on $(\mathcal{C}, \mathcal{O})$. The homotopy category, denoted $K(\textit{Mod}(\mathcal{A}, \text{d}))$, is the category whose objects are the objects of $\textit{Mod}(\mathcal{A}, \text{d})$ and whose morphisms are homotopy classes of homomorphisms of differential graded $\mathcal{A}$-modules.

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