Lemma 24.26.5. In Definition 24.26.4 the kernel of the localization functor Q : K(\textit{Mod}(\mathcal{A}, \text{d})) \to D(\mathcal{A}, \text{d}) is the category \text{Ac} of Lemma 24.26.2.
Proof. This is immediate from Derived Categories, Lemma 13.5.9 and the fact that 0 \to \mathcal{M} is a quasi-isomorphism if and only if \mathcal{M} is acyclic. \square
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