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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.