given a covering $\{ U_ i \to U\} _{i \in I}$ of $\mathcal{C}$ an object $\mathcal{F}$ of $\textit{Mod}(\mathcal{O}_ U)$ is in $\mathcal{A}_ U$ if and only if the restriction of $\mathcal{F}$ to $\mathcal{C}/U_ i$ is in $\mathcal{A}_{U_ i}$ for all $i \in I$.
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