A cocycle is a mathematical object that arises in the study of cohomology, specifically in the context of sheaf theory and Čech cohomology. It is a collection of data that satisfies certain compatibility conditions across overlapping open sets in a topological space, which helps in understanding the global properties of sheaves. Cocycles play a crucial role in defining cohomology classes, where two cocycles are considered equivalent if they differ by a coboundary.
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