Varieties of quantitative algebras as categories
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914860348997632 |
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| author | Adamek, Jiri |
| author_facet | Adamek, Jiri |
| contents | Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Varieties of quantitative algebras as categories Adamek, Jiri Category Theory 18D99 F.m Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms). |
| title | Varieties of quantitative algebras as categories |
| topic | Category Theory 18D99 F.m |
| url | https://arxiv.org/abs/2402.14662 |