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The Vietoris Monad and Weak Distributive Laws

  • Richard GarnerEmail author
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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.

Keywords

Vietoris hyperspace Monads Distributive laws Weak distributive laws Continuous lattices 

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Centre of Australian Category TheoryMacquarie UniversitySydneyAustralia

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