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On the third cohomology group of commutative monoids

Semigroup Forum volume 92, pages 511–533 (2016)Cite this article

Abstract

We interpret Grillet’s symmetric third cohomology classes of commutative monoids in terms of strictly symmetric monoidal abelian groupoids. We state and prove a classification result that generalizes the well-known one for strictly commutative Picard categories by Deligne, Fröhlich and Wall, and Sinh.

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Acknowledgments

The authors are much indebted to the referee, whose useful observations greatly improved our exposition. This work has been supported by ‘Dirección General de Investigación’ of Spain, Project: MTM2011-22554, and for the first and third authors also by FPU Grants FPU12-01112 and AP2010-3521, respectively.

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Authors and Affiliations

  1. Department of Algebra, University of Granada, 18071, Granada, Spain

    M. Calvo-Cervera, A. M. Cegarra & B. A. Heredia

Authors
  1. M. Calvo-Cervera
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  2. A. M. Cegarra
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  3. B. A. Heredia
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Corresponding author

Correspondence to A. M. Cegarra.

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Communicated by Mark V. Lawson.

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Calvo-Cervera, M., Cegarra, A.M. & Heredia, B.A. On the third cohomology group of commutative monoids. Semigroup Forum 92, 511–533 (2016). https://doi.org/10.1007/s00233-015-9696-2

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  • DOI: https://doi.org/10.1007/s00233-015-9696-2

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