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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.09264 |
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| _version_ | 1866917233516609536 |
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| author | Cappelletti, Andrea |
| author_facet | Cappelletti, Andrea |
| contents | We study the categorical-algebraic properties of the semi-abelian variety $\ell \mathbb{G}rp$ of lattice-ordered groups. In particular, we show that this category is fiber-wise algebraically cartesian closed, arithmetical, and strongly protomodular. Moreover, we observe that $\ell \mathbb{G}rp$ is not action accessible, despite the good behaviour of centralizers of internal equivalence relations. Finally, we restrict our attention to the subvariety $\ell \mathbb{A}b$ of lattice-ordered abelian groups, showing that it is algebraically coherent; this provides an example of an algebraically coherent category which is not action accessible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09264 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Categorical-Algebraic Properties of Lattice-ordered Groups Cappelletti, Andrea Category Theory We study the categorical-algebraic properties of the semi-abelian variety $\ell \mathbb{G}rp$ of lattice-ordered groups. In particular, we show that this category is fiber-wise algebraically cartesian closed, arithmetical, and strongly protomodular. Moreover, we observe that $\ell \mathbb{G}rp$ is not action accessible, despite the good behaviour of centralizers of internal equivalence relations. Finally, we restrict our attention to the subvariety $\ell \mathbb{A}b$ of lattice-ordered abelian groups, showing that it is algebraically coherent; this provides an example of an algebraically coherent category which is not action accessible. |
| title | Categorical-Algebraic Properties of Lattice-ordered Groups |
| topic | Category Theory |
| url | https://arxiv.org/abs/2310.09264 |