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  "body": "\n## Summary\n\nLet $(X, \\mathcal{O}_X)$ be a ringed space.\nA sheaf of modules on it is a sheaf of abelian groups $\\mathcal{F}$ in which each $\\mathcal{F}(U)$ is a module over $\\mathcal{O}_X(U)$, compatibly with restriction.\nIt is the sheaf-theoretic version of a module over a ring.\nVector bundles, ideal sheaves, quasi-coherent and coherent sheaves are all sheaves of modules.\n\n## Explanations\n\n### L1 human\n\nOn a space, the functions on each open set form a ring.\nA sheaf of modules attaches to each open set a module over that ring, in a way that is compatible with shrinking the open set.\nThe simplest example is the sheaf of functions itself.\nAnother example is the sheaf of vector fields on a manifold: one can multiply a vector field by a function and get a vector field.\n",
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