The cap product in sheaf cohomology is an operation that combines a cohomology class from a sheaf with a class in a homology group, resulting in a new cohomology class. This operation is vital for understanding the interaction between topology and algebraic geometry, as it allows for the computation of intersection numbers and various dualities within the framework of sheaf theory. The cap product also establishes a connection between cohomology and homology, making it an essential tool in algebraic topology.
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