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On extension of functors to the Kleisli category of some weakly normal monads. (English) Zbl 0852.54023
The author considers various monads $$T$$ of the category $$\mathcal C$$ of compact Hausdorff spaces (all related to the inclusion hyperspace monad) and investigates the question when an endofunctor of $$\mathcal C$$ admits an “extension” to an endofunctor of the Kleisli category $${\mathcal C}_T$$ along the free functor $${\mathcal C} \to {\mathcal C}_T$$. Sufficient conditions for a negative answer are presented.
##### MSC:
 54D30 Compactness 54B30 Categorical methods in general topology 18C20 Eilenberg-Moore and Kleisli constructions for monads
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