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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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