Cohomology of Presheaves of Monoids
| Autor: | P. Carrasco, Antonio M. Cegarra |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Monoid
Pure mathematics Homotopy colimit General Mathematics monoidal prestack 0102 computer and information sciences Topological space Presheaf of monoids Mathematics::Algebraic Topology 01 natural sciences Cohomology Mathematics::K-Theory and Homology Mathematics::Category Theory simplicial set homotopy colimit Computer Science (miscellaneous) presheaf of monoids 0101 mathematics Abelian group Engineering (miscellaneous) Mathematics Group (mathematics) lcsh:Mathematics 010102 general mathematics Monoidal prestack simplicial set lcsh:QA1-939 Simplicial set 010201 computation theory & mathematics Computer Science::Programming Languages cohomology homotopy colimit |
| Zdroj: | Mathematics, Vol 8, Iss 1, p 116 (2020) Mathematics Volume 8 Issue 1 Digibug. Repositorio Institucional de la Universidad de Granada instname |
| ISSN: | 2227-7390 |
| DOI: | 10.3390/math8010116 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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