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Cohomology of Presheaves of Monoids

Department Algebra, University of Granada, 18071 Granada, Spain
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 116;
Received: 19 December 2019 / Revised: 7 January 2020 / Accepted: 9 January 2020 / Published: 12 January 2020
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 .
Keywords: cohomology; presheaf of monoids; monoidal prestack; simplicial set, homotopy colimit cohomology; presheaf of monoids; monoidal prestack; simplicial set, homotopy colimit
MDPI and ACS Style

Carrasco, P.; Cegarra, A.M. Cohomology of Presheaves of Monoids. Mathematics 2020, 8, 116.

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