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|elliptic]] cohomology, [[ | + | 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]] | ||
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, equivariant cohomology, and hyperbolic cohomology of infinite Abelian groups.