Abelian group theory | Functors | Homology theory | Algebraic geometry | Cohomology theories

Bivariant theory

In mathematics, a bivariant theory was introduced by Fulton and MacPherson, in order to put a ring structure on the Chow group of a singular variety, the resulting ring called an operational Chow ring. On technical levels, a bivariant theory is a mix of a homology theory and a cohomology theory. In general, a homology theory is a covariant functor from the category of spaces to the category of abelian groups, while a cohomology theory is a contravariant functor from the category of (nice) spaces to the category of rings. A bivariant theory is a functor both covariant and contravariant; hence, the name “bivariant”. (Wikipedia).

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Related pages

Functor | Cohomology | Homology (mathematics) | Chow group | Covariance and contravariance (computer science) | Abelian group