Definition 17.4.1. Let (X, \mathcal{O}_ X) be a ringed space. Let \mathcal{F} be a sheaf of \mathcal{O}_ X-modules. We say that \mathcal{F} is generated by global sections if there exist a set I, and global sections s_ i \in \Gamma (X, \mathcal{F}), i \in I such that the map
\bigoplus \nolimits _{i \in I} \mathcal{O}_ X \longrightarrow \mathcal{F}
which is the map associated to s_ i on the summand corresponding to i, is surjective. In this case we say that the sections s_ i generate \mathcal{F}.
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