Definition 7.7.6 (00VR)—The Stacks project

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Definition 7.7.6. Let $\mathcal{C}$ be a site, let $\mathcal{A}$ be a category and let $\mathcal{F}$ be a presheaf on $\mathcal{C}$ with values in $\mathcal{A}$. We say that $\mathcal{F}$ is a sheaf if for all objects $X$ of $\mathcal{A}$ the presheaf of sets $\mathcal{F}_ X$ (defined above) is a sheaf.

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