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arXiv · 2511.06502

Poset-enriched categories and free exact completions

Vasileios Aravantinos-Sotiropoulos
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Abstract

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.

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Vasileios Aravantinos-Sotiropoulos. 2025-11-09. Poset-enriched categories and free exact completions. https://arxiv.org/abs/2511.06502

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