Poset-enriched categories and free exact completions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915674226425856 |
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| author | Aravantinos-Sotiropoulos, Vasileios |
| author_facet | Aravantinos-Sotiropoulos, Vasileios |
| contents | We give an elementary construction of the exact completion of a weakly lex category for categories enriched in the cartesian closed category $\mathsf{Pos}$ of partially ordered sets. Paralleling the ordinary case, we characterize categories which arise as such completions in terms of projective objects. We then apply the results to categories of Eilenberg-Moore algebras for monads on $\mathsf{Pos}$. In particular, we show that every variety of ordered algebras is the exact completion of a subcategory on certain free algebras, thereby answering a question of A. Kurz and J. Velebil. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poset-enriched categories and free exact completions Aravantinos-Sotiropoulos, Vasileios Category Theory We give an elementary construction of the exact completion of a weakly lex category for categories enriched in the cartesian closed category $\mathsf{Pos}$ of partially ordered sets. Paralleling the ordinary case, we characterize categories which arise as such completions in terms of projective objects. We then apply the results to categories of Eilenberg-Moore algebras for monads on $\mathsf{Pos}$. In particular, we show that every variety of ordered algebras is the exact completion of a subcategory on certain free algebras, thereby answering a question of A. Kurz and J. Velebil. |
| title | Poset-enriched categories and free exact completions |
| topic | Category Theory |
| url | https://arxiv.org/abs/2511.06502 |