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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