nLab cohomology ring

Contents

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

Given any generalized (Eilenberg-Steenrod) cohomology theory EE, then for each topological space XX, there is, by definition, the graded abelian group

E (X)Ab . E^\bullet(X) \in Ab^{\mathbb{Z}} \,.

This is the EE-cohomology group of XX. Now if EE is a multiplicative cohomology theory, then these groups inherit the structure of rings. As such

E (X)Ring E^\bullet(X) \in Ring^{\mathbb{Z}}

is the EE-cohomology ring of XX.

Analogously for various suitable generalizations of the nature of EE and XX (see at generalized cohomology).

References

Implementation of ordinary\;cohomology rings in cubical agda:

Last revised on July 5, 2023 at 18:02:58. See the history of this page for a list of all contributions to it.