Definition 24.33.1 (0GZ9)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 24: Differential Graded Sheaves
Section 24.33: Differential graded modules on a category
Definition 24.33.1 (cite)

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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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