Definition 22.22.2. Let $(A, \text{d})$ be a differential graded algebra. Let $\text{Ac}$ and $\text{Qis}$ be as in Lemma 22.22.1. The derived category of $(A, \text{d})$ is the triangulated category

$D(A, \text{d}) = K(\text{Mod}_{(A, \text{d})})/\text{Ac} = \text{Qis}^{-1}K(\text{Mod}_{(A, \text{d})}).$

We denote $H^0 : D(A, \text{d}) \to \text{Mod}_ R$ the unique functor whose composition with the quotient functor gives back the functor $H^0$ defined above.

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