Lemma 18.32.5. Let $(\mathcal{C}, \mathcal{O})$ be a ringed space. There exists a set of invertible modules $\{ \mathcal{L}_ i\} _{i \in I}$ such that each invertible module on $(\mathcal{C}, \mathcal{O})$ is isomorphic to exactly one of the $\mathcal{L}_ i$.

**Proof.**
Omitted, but see Sheaves of Modules, Lemma 17.25.8.
$\square$

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