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.

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Vietoris Monad 和弱分配法

紧致豪斯多夫空间范畴上的 Vietoris 单子是集合范畴上幂集单子的拓扑类似物。利用 Manes 将紧致 Hausdorff 空间表征为集合上超滤单子的代数，我们通过展示 Vietoris monad 给出了上述类比的精确形式，该类比是由幂集的 Böhm 意义上的弱分配律引起的超滤单子之上的单子。