In mathematics, a **sheaf** is a fundamental concept in the fields of topology and algebraic geometry that provides a way to systematically track local data attached to the open sets of a topological space. The idea is to gather local information and then piece it together to understand global properties.
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A sheaf of sets is a presheaf in which compatible sections on any open cover glue to one unique section on the union.
A sheaf may additionally carry abelian group or module structure on its sections, with restriction and gluing preserving that structure. The underlying sheaf of sets retains the same local-to-global axiom.