The Vietoris monad and weak distributive laws

Richard Garner*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    6 Citations (Scopus)
    2 Downloads (Pure)

    Abstract

    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
    Volume28
    Issue number2
    Early online date16 Oct 2019
    DOIs
    Publication statusPublished - Apr 2020

    Keywords

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

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