Definition 13.13.5. Let \mathcal{A} be an abelian category. Let \text{FAc}(\mathcal{A}) and \text{FQis}(\mathcal{A}) be as in Lemma 13.13.4. The filtered derived category of \mathcal{A} is the triangulated category
DF(\mathcal{A}) = K(\text{Fil}^ f(\mathcal{A}))/\text{FAc}(\mathcal{A}) = \text{FQis}(\mathcal{A})^{-1} K(\text{Fil}^ f(\mathcal{A})).
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