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