Lemma 24.26.6. In Definition 24.26.4 the functor $H^0 : K(\textit{Mod}(\mathcal{A}, \text{d})) \to \textit{Mod}(\mathcal{O})$ factors through a homological functor $H^0 : D(\mathcal{A}, \text{d}) \to \textit{Mod}(\mathcal{O})$.

**Proof.**
Follows immediately from Derived Categories, Lemma 13.5.7.
$\square$

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