Cohomology of Presheaves of Monoids
Metadatos
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MDPI
Materia
Cohomology Presheaf of monoids Monoidal prestack Simplicial set Homotopy colimit
Date
2020-01-12Referencia bibliográfica
Carrasco, P.; Cegarra, A.M. Cohomology of Presheaves of Monoids. Mathematics 2020, 8, 116. [doi:10.3390/math8010116]
Résumé
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.