Difference between revisions of "Cohomology"
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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 [[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]]. | ||
| − | Well-known examples include [[de Rham cohomology]] in [[differential geometry]], [[elliptic curve]] cohomology, and [[Hyperbola|hyperbolic]] cohomology of infinite [[Abelian]] [[Group (mathematics)|groups]]. | + | 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]]. |
[[Category:Algebra]] | [[Category:Algebra]] | ||
Latest revision as of 04:19, November 11, 2011
In category theory, the cohomology of an exact sequence studies the relationship between the cokernels and coimages, when it is possible to take their quotient. Cohomology is the category-theoretic dual of homology.
Well-known examples include de Rham cohomology in differential geometry, elliptic cohomology, equivariant cohomology, and hyperbolic cohomology of infinite Abelian groups.
