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Mathematics 2015, 3(4), 1001-1031; doi:10.3390/math3041001

A Cohomology Theory for Commutative Monoids

Departamento de Álgebra, Universidad de Granada, 18071 Granada, Spain
Author to whom correspondence should be addressed.
Academic Editor: Indranil SenGupta
Received: 21 September 2015 / Revised: 15 October 2015 / Accepted: 16 October 2015 / Published: 27 October 2015
(This article belongs to the Special Issue Homological and Homotopical Algebra and Category Theory)
View Full-Text   |   Download PDF [351 KB, uploaded 4 November 2015]


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. View Full-Text
Keywords: commutative monoid; cohomology; simplicial set; braided monoidal category commutative monoid; cohomology; simplicial set; braided monoidal category
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Calvo-Cervera, M.; Cegarra, A.M. A Cohomology Theory for Commutative Monoids. Mathematics 2015, 3, 1001-1031.

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