Duality for coalgebras for Vietoris and monadicity

Abbadini, Marco;Di Liberti, Ivan
(2025) The Journal of Symbolic Logic — Vol. 90, n° 3, p. 1022-1055 (2025)

Files

2025AbbDiL-Dualityforcoalgebrasforvietorisandmonadicity.pdf
  • Open Access
  • Adobe PDF
  • 437.84 KB
Download

Details

Authors
Abstract
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 Jónsson-Tarski duality for modal algebras beyond the 0-dimensional setting.
Affiliations
  • University of Birmingham
  • Stockholm University

Citations

  • APA
  • Chicago
  • FWB

Abbadini, M., & Di Liberti, I. (2025). Duality for coalgebras for Vietoris and monadicity. The Journal of Symbolic Logic, 90(3), 1022-1055. https://doi.org/10.1017/jsl.2024.14 (Original work published 2025)