Definition 24.33.1. In the situation above, we denote *$\mathit{QC}(\mathcal{A}, \text{d})$* the full subcategory of $D(\mathcal{A}, \text{d})$ consisting of objects $M$ such that for all $U \to V$ in $\mathcal{C}$ the canonical map

\[ R\Gamma (V, M) \otimes _{\mathcal{A}(V)}^\mathbf {L} \mathcal{A}(U) \longrightarrow R\Gamma (U, M) \]

is an isomorphism in $D(\mathcal{A}(U), \text{d})$.

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