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A Cohomology Theory for Commutative Monoids

Departamento de Álgebra, Universidad de Granada, 18071 Granada, Spain
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Academic Editor: Indranil SenGupta
Mathematics 2015, 3(4), 1001-1031; https://doi.org/10.3390/math3041001
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)
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
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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