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Definition 22.5.3. Let $(A, \text{d})$ be a differential graded algebra. The homotopy category, denoted $K(\text{Mod}_{(A, \text{d})})$, is the category whose objects are the objects of $\text{Mod}_{(A, \text{d})}$ and whose morphisms are homotopy classes of homomorphisms of differential graded $A$-modules.

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View Definition 22.5.3 as pdf