A Cohomology Theory for Commutative Monoids

María Calvo-Cervera and Antonio M. Cegarra
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María Calvo-Cervera: Departamento de Álgebra, Universidad de Granada, 18071 Granada, Spain
Antonio M. Cegarra: Departamento de Álgebra, Universidad de Granada, 18071 Granada, Spain

Mathematics, 2015, vol. 3, issue 4, 1-31

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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