The Vietoris monad and weak distributive laws

Richard Garner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
4 Downloads (Pure)


The Vietoris monad on the category of compact Hausdorff spaces is a topological analogue of the power-set monad on the category of sets. Exploiting Manes' characterisation of the compact Hausdorff spaces as algebras for the ultrafilter monad on sets, we give precise form to the above analogy by exhibiting the Vietoris monad as induced by a weak distributive law, in the sense of Böhm, of the power-set monad over the ultrafilter monad.

Original languageEnglish
Pages (from-to)339-354
Number of pages16
JournalApplied Categorical Structures
Issue number2
Early online date16 Oct 2019
Publication statusPublished - Apr 2020


  • Vietoris hyperspace
  • Monads
  • Distributive laws
  • Weak distributive laws
  • Continuous lattices

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