2025/11/09 by Vasileios Aravantinos-Sotiropoulos, Aravantinos-Sotiropoulos, Vasileios
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2511.06502
We give an elementary construction of the exact completion of a weakly lex category for categories enriched in the cartesian closed category 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 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.