Cohomology groups are algebraic structures associated with topological spaces that provide a way to classify and measure their shape and features. They arise from the study of cochain complexes, where cochains are functions that assign values to the open sets of a space, allowing for an analysis of continuity and connectivity. These groups are crucial in algebraic topology as they capture information about the topology of a space, such as holes and obstructions, and can be computed using tools like Kan extensions.
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