Cohomology of Presheaves of Monoids Carrasco Carrasco, María Del Pilar Martínez Cegarra, Antonio Cohomology Presheaf of monoids Monoidal prestack Simplicial set Homotopy colimit This research received external funding from FQM-379: Algebra y Teoría de la Información 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. 2020-03-25T08:41:47Z 2020-03-25T08:41:47Z 2020-01-12 journal article Carrasco, P.; Cegarra, A.M. Cohomology of Presheaves of Monoids. Mathematics 2020, 8, 116. [doi:10.3390/math8010116] http://hdl.handle.net/10481/60606 10.3390/math8010116 eng http://creativecommons.org/licenses/by/3.0/es/ open access Atribución 3.0 España MDPI