Definition 28.23.1. Let (X, \mathcal{O}_ X) be a ringed space. Let \kappa be an infinite cardinal. We say a sheaf of \mathcal{O}_ X-modules \mathcal{F} is \kappa -generated if there exists an open covering X = \bigcup U_ i such that \mathcal{F}|_{U_ i} is generated by a subset R_ i \subset \mathcal{F}(U_ i) whose cardinality is at most \kappa .
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