The sheaf condition is a fundamental property that a sheaf must satisfy, ensuring that local data can be uniquely glued together to form global data. This condition requires that if you have local sections defined on an open cover of a space, and these sections agree on overlaps of the cover, then there exists a unique global section that corresponds to these local sections. This concept is essential in the study of sheaves, as it establishes the coherence needed for understanding how local information relates to global structures.
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