Rectangular torsion theories
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912305314267136 |
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| author | Caviglia, Elena Janelidze, Zurab Mesiti, Luca |
| author_facet | Caviglia, Elena Janelidze, Zurab Mesiti, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01057 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rectangular torsion theories Caviglia, Elena Janelidze, Zurab Mesiti, Luca Category Theory 18E40 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. |
| title | Rectangular torsion theories |
| topic | Category Theory 18E40 |
| url | https://arxiv.org/abs/2504.01057 |