Partial algebras and implications of (weak) matrix properties
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913324146360320 |
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| author | Hoefnagel, Michael Jacqmin, Pierre-Alain |
| author_facet | Hoefnagel, Michael Jacqmin, Pierre-Alain |
| contents | Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications $M\Rightarrow N$ between them. We show here that this algorithm reduces to construct a partial term corresponding to $N$ from a partial term corresponding to $M$. Moreover, we prove that this is further equivalent to the corresponding implication between the weak versions of these properties, i.e., the one where only strong monomorphisms are considered instead of all monomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14166 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partial algebras and implications of (weak) matrix properties Hoefnagel, Michael Jacqmin, Pierre-Alain Category Theory 03B35, 18E13, 08A55, 08B05, 18-08, 18B15, 18A20 Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algorithm has been developed to determine implications $M\Rightarrow N$ between them. We show here that this algorithm reduces to construct a partial term corresponding to $N$ from a partial term corresponding to $M$. Moreover, we prove that this is further equivalent to the corresponding implication between the weak versions of these properties, i.e., the one where only strong monomorphisms are considered instead of all monomorphisms. |
| title | Partial algebras and implications of (weak) matrix properties |
| topic | Category Theory 03B35, 18E13, 08A55, 08B05, 18-08, 18B15, 18A20 |
| url | https://arxiv.org/abs/2404.14166 |