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.
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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