Rectangular torsion theories

Elena Caviglia; Zurab Janelidze; Luca Mesiti

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arXiv · 2504.01057

Rectangular torsion theories

Elena Caviglia·Zurab Janelidze·Luca Mesiti

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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.

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Elena Caviglia, Zurab Janelidze, Luca Mesiti. 2025-04-01. Rectangular torsion theories. https://arxiv.org/abs/2504.01057

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