A Cohomology Theory for Commutative Monoids

Abstract

Extending Eilenberg–Mac Lane’s cohomology of abelian groups, a cohomology theory is introduced for commutative monoids. The cohomology groups in this theory agree with the pre-existing ones by Grillet in low dimensions, but they differ beyond dimension two. A natural interpretation is given for the three-cohomology classes in terms of braided monoidal groupoids.

Keywords

• commutative monoid
• cohomology
• simplicial set
• braided monoidal category