Next Article in Journal
Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains
Previous Article in Journal
Quantum Linear Scalar Fields with Time Dependent Potentials: Overview and Applications to Cosmology
Open AccessArticle

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; https://doi.org/10.3390/math8010116
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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop