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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