The Stacks project

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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