Cohomology is a fundamental concept in algebraic topology and other fields of mathematics that studies the properties of spaces through algebraic invariants. It provides a way to associate a sequence of abelian groups or vector spaces to a topological space, which can help in understanding its structure and features.
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Cohomology is the contravariant counterpart of homology, formed from cochains and coboundaries. A coefficient ring equips it with the cup product and hence with a graded ring structure.