Pretorsion theories in general categories
| Autor: | Carmelo Antonio Finocchiaro, Marino Gran, Alberto Facchini |
|---|---|
| Přispěvatelé: | UCL - SST/IRMP - Institut de recherche en mathématique et physique |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Commutative Algebra (math.AC) Torsion theory 01 natural sciences Morphism Non-abelian torsion theory Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Ideal of morphisms Category Theory (math.CT) 0101 mathematics Abelian group Finite set Mathematics Subcategory Algebra and Number Theory 010102 general mathematics Mathematics - Category Theory Mathematics - Rings and Algebras Mathematics - Commutative Algebra 18E40 18D20 17A65 13D30 Category of preordered sets Pretorsion theory Rings and Algebras (math.RA) Torsion (algebra) 010307 mathematical physics |
| Zdroj: | Journal of Pure and Applied Algebra, Vol. 25, no.2, p. 106503 (2021) |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2020.106503 |
| Popis: | We present a setting for the study of torsion theories in general categories. The idea is to associate, with any pair ($\mathcal T$, $\mathcal F$) of full replete subcategories in a category $\mathcal C$, the corresponding full subcategory $\mathcal Z = \mathcal T \cap \mathcal F$ of \emph{trivial objects} in $\mathcal C$. The morphisms which factor through $\mathcal Z$ are called $\mathcal Z$-trivial, and these form an ideal of morphisms, with respect to which one can define $\mathcal Z$-prekernels, $\mathcal Z$-precokernels, and short $\mathcal Z$-preexact sequences. This naturally leads to the notion of pretorsion theory, which is the object of study of this article, and includes the classical one in the abelian context when $\mathcal Z$ is reduced to the $0$-object of $\mathcal C$. We study the basic properties of pretorsion theories, and examine some new examples in the category of all endomappings of finite sets and in the category of preordered sets. 22 pages |
| Databáze: | OpenAIRE |
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