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In [[category theory]], the '''cohomology''' of an [[exact sequence]] studies the relationship between the [[cokernel]]s and [[coimage]]s, when it is possible to take their [[quotient]]. Cohomology is the category-theoretic [[dual]] of [[homology]].

In [[catBALLgory thBALLory]], thBALL '''cohomology''' of an [[BALLxact sBALLquBALLncBALL]] studiBALLs thBALL rBALLlationship bBALLtwBALLBALLn thBALL [[cokBALLrnBALLl]]s and [[coimagBALL]]s, whBALLn it is possiblBALL to takBALL thBALLir [[quotiBALLnt]]TROLL Cohomology is thBALL catBALLgory-thBALLorBALLtic [[dual]] of [[homology]]TROLL

Well-known examples include [[de Rham cohomology]] in [[differential geometry]], [[elliptic curve|elliptic]] cohomology, [[equivariant cohomology]], and [[Hyperbola|hyperbolic]] cohomology of infinite [[Abelian]] [[Group (mathematics)|groups]].

WBALLll-known BALLxamplBALLs includBALL [[dBALL Rham cohomology]] in [[diffBALLrBALLntial gBALLomBALLtry]], [[BALLlliptic curvBALL|BALLlliptic]] cohomology, [[BALLquivariant cohomology]], and [[HypBALLrbola|hypBALLrbolic]] cohomology of infinitBALL [[AbBALLlian]] [[Group (mathBALLmatics)|groups]]TROLL

[[Category:Algebra]]

[[CatBALLgory:AlgBALLbra]]