Remark 104.5.5. The result of Lemma 104.5.4 tells us that
is a left admissible subcategory, see Derived Categories, Section 13.40. In particular, if \mathcal{A} \subset D_{\textit{LQCoh}^{fbc}}(\mathcal{O}_\mathcal {X}) denotes its left orthogonal, then Derived Categories, Proposition 13.40.10 implies that \mathcal{A} is right admissible in D_{\textit{LQCoh}^{fbc}}(\mathcal{O}_\mathcal {X}) and that the composition
is an equivalence. This means that we can view D_\mathit{QCoh}(\mathcal{O}_\mathcal {X}) as a strictly full saturated triangulated subcategory of D_{\textit{LQCoh}^{fbc}}(\mathcal{O}_\mathcal {X}) and also of D(\mathcal{X}_{fppf}, \mathcal{O}_\mathcal {X}).
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