Difference between revisions of "Cohomology"

Revision as of 21:07, November 17, 2008

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 curve cohomology, and hyperbolic cohomology of infinite Abelian groups.

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-In [[Category_theory|category theory]], the '''cohomology''' of an [[Exact_sequence|exact sequence]] studies the relationship between the [[Cokernel|cokernels]] and [[Coimages|coimage]], when it is possible to take their [[Quotient|quotient]]. Cohomology is the category-theoretic [[Dual|dual]] of [[Homology|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|de Rham cohomology]] in [[Differential_geometry|differential geometry]], [[Elliptic_curve|elliptic curve]] cohomology, and [[Hyperbola|hyperbolic]] cohomology of infinite [[Abelian]] [[Group|groups]].
+Well-known examples include [[de Rham cohomology]] in [[differential geometry]], [[elliptic curve]] cohomology, and [[Hyperbola|hyperbolic]] cohomology of infinite [[Abelian]] [[Group (mathematics)|groups]].
 [[Category:Algebra]]