Torsion theories and coverings of preordered groups
| Autor: | Marino Gran, Aline Michel |
|---|---|
| Přispěvatelé: | UCL - SST/IRMP - Institut de recherche en mathématique et physique |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Galois theory Structure (category theory) 0102 computer and information sciences 01 natural sciences Torsion theory Mathematics::K-Theory and Homology Mathematics::Category Theory FOS: Mathematics Order (group theory) Category Theory (math.CT) Preordered groups 0101 mathematics Algebra over a field Mathematics Subcategory Algebra and Number Theory 010102 general mathematics Mathematics - Category Theory Mathematics - Rings and Algebras Factorization system Rings and Algebras (math.RA) 010201 computation theory & mathematics Torsion (algebra) 18E40 18E50 06F15 18A40 |
| Zdroj: | Algebra Universalis, Vol. 82, no. 22, p. https://doi.org/10.1007/s00012-021-00709-6 (19 February 2021) |
| DOI: | 10.1007/s00012-021-00709-6 |
| Popis: | In this article we explore a non-abelian torsion theory in the category of preordered groups: the objects of its torsion-free subcategory are the partially ordered groups, whereas the objects of the torsion subcategory are groups (with the total order). The reflector from the category of preordered groups to this torsion-free subcategory has stable units, and we prove that it induces a monotone-light factorization system. We describe the coverings relative to the Galois structure naturally associated with this reflector, and explain how these coverings can be classified as internal actions of a Galois groupoid. Finally, we prove that in the category of preordered groups there is also a pretorsion theory, whose torsion subcategory can be identified with a category of internal groups. This latter is precisely the subcategory of protomodular objects in the category of preordered groups, as recently discovered by Clementino, Martins-Ferreira, and Montoli. 21 pages, minor changes and improvements |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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