2023/02/19 by Marco Abbadini, Abbadini, Marco, Ivan Di Liberti +1
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2302.09529
openalex publication_date 2023/02/19 · openalex created_date 2023/02/22 · openalex updated_date 2026/08/01
We prove that the opposite of the category of coalgebras for the Vietoris endofunctor on the category of compact Hausdorff spaces is monadic over Set. We deliver an analogous result for the upper, lower and convex Vietoris endofunctors acting on the category of stably compact spaces. We provide axiomatizations of the associated (infinitary) varieties. This can be seen as a version of Jonsson-Tarski duality for modal algebras beyond the 0-dimensional setting.