Rectangular torsion theories

In this paper we introduce and study \emph{rectangular torsion theories}, i.e.\ those torsion theories $(\C,\T,\F)$ with $\C$ a pointed category, where the canonical functor $\C\to \T\times\F$ is an equivalence of categories. In particular, we show that these are precisely the internal rectangular bands in the 2-category of pointed categories.

Publication Details

Journal
ArXiv.org
Published
2025-04-01
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
article
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article

Rectangular torsion theories

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
article

Rectangular torsion theories

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Abstract

In this paper we introduce and study \emph{rectangular torsion theories}, i.e.\ those torsion theories $(\C,\T,\F)$ with $\C$ a pointed category, where the canonical functor $\C\to \T\times\F$ is an equivalence of categories. In particular, we show that these are precisely the internal rectangular bands in the 2-category of pointed categories.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 47%
Homotopy and Cohomology in Algebraic Topology
Open Access PDFOpenAlex
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Rectangular torsion theories · ArXiv.org (2025) | TGRS Research Map | TGRS