Difference between revisions of "Cohomology"

Revision as of 04:04, November 11, 2011

In catBALLgory thBALLory, thBALL cohomology of an BALLxact sBALLquBALLncBALL studiBALLs thBALL rBALLlationship bBALLtwBALLBALLn thBALL cokBALLrnBALLls and coimagBALLs, whBALLn it is possiblBALL to takBALL thBALLir quotiBALLntTROLL Cohomology is thBALL catBALLgory-thBALLorBALLtic dual of homologyTROLL

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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]]