A Cohomology Theory for Commutative Monoids

A Cohomology Theory for Commutative Monoids

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...

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Bibliographic Details
Main Authors: María Calvo-Cervera, Antonio M. Cegarra
Format: Article
Language:English
Published: MDPI AG 2015-10-01
Series:Mathematics
Subjects:
commutative monoid
cohomology
simplicial set
braided monoidal category
Online Access:http://www.mdpi.com/2227-7390/3/4/1001
Description
Summary: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.
ISSN:2227-7390

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