nLab
multiplicative cohomology theory

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

A cohomology theory EE is called multiplicative if E (X)E^\bullet(X) is not just a graded abelian group, but actually a graded ring.

Definition

A multiplicative structure on a generalized (Eilenberg-Steenrod) cohomology theory is the structure of a ring spectrum on the spectrum that represents it.

e.g. Lurie 10, lecture 4

In particular every E-∞ ring is a ring spectrum, hence represents a multiplicative cohomology theory, but the converse is in general false.

Examples

For multiplicative cohomology theories one can consider

See also

References

Revised on February 26, 2016 15:29:41 by Urs Schreiber (194.210.233.5)