Cohomology operations are algebraic tools used in algebraic topology and related fields to study the properties of topological spaces through their cohomology groups. Cohomology itself is a mathematical concept that associates a series of abelian groups or vector spaces with a topological space, capturing information about its structure and features.
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A cohomology operation is a natural transformation between cohomology functors. Thus for every continuous map , its pullback commutes with the operation: . This makes operations additional invariants of homotopy equivalence, beyond the additive groups and their cup products.