Difference between revisions of "Cohomology"
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m (It's called "elliptic cohomology", not "elliptic curve cohomology". There is a connected to elliptic curves, so leaving the link.) |
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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|elliptic]] 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, [[equivaiant cohomology]], and [[Hyperbola|hyperbolic]] cohomology of infinite [[Abelian]] [[Group (mathematics)|groups]]. |
[[Category:Algebra]] | [[Category:Algebra]] | ||
Revision as of 19:46, February 16, 2009
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, equivaiant cohomology, and hyperbolic cohomology of infinite Abelian groups.