nLab
multiplicative cohomology theory

Idea

A cohomology theory $E$ is called multiplicative if $E^{•}(X)$ is not just a graded abelian group, but actually a graded ring.

This is in particular the case when the spectrum $E$ representing the cohomology theory is an E-∞ ring spectrum.

Examples

• integral cohomology

• topological K-theory, K-theory

• tmf

• etc.

Related entries

For multiplicative cohomology theories one can consider

• universal coefficient theorem, module cohomology theories, …

See also

• Thom isomorphism

• orientation in generalized cohomology

• fiber integration

• K-theory of a bipermutative category

• A Survey of Elliptic Cohomology - cohomology theories