Categories which are varieties of classical or ordered algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917595687419904 |
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| author | Adamek, Jiri |
| author_facet | Adamek, Jiri |
| contents | Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous characterization of varieties of ordered algebras is also presented. We work with order-enriched categories, and introduce the concept of subexact category and subregular projective (corresponding naturally to the ordinary case). Varieties of ordered algebras are precisely the subexact categories with a subvarietal generator. This means a strong generator which is abstractly finite and subregularly projective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14557 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Categories which are varieties of classical or ordered algebras Adamek, Jiri Category Theory 18D99 Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous characterization of varieties of ordered algebras is also presented. We work with order-enriched categories, and introduce the concept of subexact category and subregular projective (corresponding naturally to the ordinary case). Varieties of ordered algebras are precisely the subexact categories with a subvarietal generator. This means a strong generator which is abstractly finite and subregularly projective. |
| title | Categories which are varieties of classical or ordered algebras |
| topic | Category Theory 18D99 |
| url | https://arxiv.org/abs/2402.14557 |