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The Stacks project

Definition 59.11.4. We denote $\mathop{\mathit{Sh}}\nolimits (\mathcal{C})$ (resp. $\textit{Ab}(\mathcal{C})$) the full subcategory of $\textit{PSh}(\mathcal{C})$ (resp. $\textit{PAb}(\mathcal{C})$) whose objects are sheaves. This is the category of sheaves of sets (resp. abelian sheaves) on $\mathcal{C}$.

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View Definition 59.11.4 as pdf