cohomology

# Contents

## Idea

A cohomology theory $E$ is called multiplicative if $E^\bullet(X)$ 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.

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