A note on the atomicity of arithmeticity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909071107424256 |
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| author | Hoefnagel, Michael Jacqmin, Pierre-Alain |
| author_facet | Hoefnagel, Michael Jacqmin, Pierre-Alain |
| contents | The main aim of this note is to show that, in the regular context, every matrix property in the sense of Z. Janelidze either implies the Mal'tsev property, or is implied by the majority property. When the regular category is arithmetical, i.e., both Mal'tsev and a majority category, then we show that satisfies every non-trivial matrix property. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_06414 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the atomicity of arithmeticity Hoefnagel, Michael Jacqmin, Pierre-Alain Category Theory 18E13, 08B05, 18E08, 08A05, 06-08 The main aim of this note is to show that, in the regular context, every matrix property in the sense of Z. Janelidze either implies the Mal'tsev property, or is implied by the majority property. When the regular category is arithmetical, i.e., both Mal'tsev and a majority category, then we show that satisfies every non-trivial matrix property. |
| title | A note on the atomicity of arithmeticity |
| topic | Category Theory 18E13, 08B05, 18E08, 08A05, 06-08 |
| url | https://arxiv.org/abs/2401.06414 |