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Submonads of the capacity monad. (English) Zbl 1174.18301

Summary: Two subfunctors of the capacity functor in the category of compacta, namely the functors of cap-capacities and cup-capacities (also known as sup-measures), are introduced. It is proved that these functors generate submonads of the capacity monad, and each capacity on a compact Hausdorff space is the image under the multiplication of the capacity monad of a cup-capacity with support in a subspace of cap-capacities.

MSC:

18B30 Categories of topological spaces and continuous mappings (MSC2010)
54B30 Categorical methods in general topology
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