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Cohomology of Presheaves of Monoids

Author

Listed:
  • Pilar Carrasco

    (Department Algebra, University of Granada, 18071 Granada, Spain)

  • Antonio M. Cegarra

    (Department Algebra, University of Granada, 18071 Granada, Spain)

Abstract

The purpose of this work is to extend Leech cohomology for monoids (and so Eilenberg-Mac Lane cohomology of groups) to presheaves of monoids on an arbitrary small category. The main result states and proves a cohomological classification of monoidal prestacks on a category with values in groupoids with abelian isotropy groups. The paper also includes a cohomological classification for extensions of presheaves of monoids, which is useful to the study of H -extensions of presheaves of regular monoids. The results apply directly in several settings such as presheaves of monoids on a topological space, simplicial monoids, presheaves of simplicial monoids on a topological space, monoids or simplicial monoids on which a fixed monoid or group acts, and so forth.

Suggested Citation

  • Pilar Carrasco & Antonio M. Cegarra, 2020. "Cohomology of Presheaves of Monoids," Mathematics, MDPI, vol. 8(1), pages 1-35, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:116-:d:307959
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