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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2208.12597 |
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| _version_ | 1866913444038443008 |
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| author | Lapenta, Serafina Metere, Giuseppe Spada, Luca |
| author_facet | Lapenta, Serafina Metere, Giuseppe Spada, Luca |
| contents | Let $A$ be a homological category and $U\colon B\to A$ be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to $U$, and we show that, under suitable conditions, any object of $A$ can be seen as a relative ideal of some object in $B$. We then develop a case study. We first prove that the category of hoops is semi-abelian and that the category of MV-algebras is protomodular, then we apply our results to the forgetful functor from the category of MV-algebras to the category of Wajsberg hoops. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12597 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Relative ideals in homological categories, with an application to MV-algebras Lapenta, Serafina Metere, Giuseppe Spada, Luca Category Theory Let $A$ be a homological category and $U\colon B\to A$ be a faithful conservative right adjoint. We introduce the notion of relative ideal with respect to $U$, and we show that, under suitable conditions, any object of $A$ can be seen as a relative ideal of some object in $B$. We then develop a case study. We first prove that the category of hoops is semi-abelian and that the category of MV-algebras is protomodular, then we apply our results to the forgetful functor from the category of MV-algebras to the category of Wajsberg hoops. |
| title | Relative ideals in homological categories, with an application to MV-algebras |
| topic | Category Theory |
| url | https://arxiv.org/abs/2208.12597 |