Hlushak, I. D.; Nykyforchyn, O. R. Submonads of the capacity monad. (English) Zbl 1174.18301 Carpathian J. Math. 24, No. 1, 56-67 (2008). 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. Cited in 2 Documents MSC: 18B30 Categories of topological spaces and continuous mappings (MSC2010) 54B30 Categorical methods in general topology Keywords:capacity functor; category of compacta; monad (triple); submonad PDFBibTeX XMLCite \textit{I. D. Hlushak} and \textit{O. R. Nykyforchyn}, Carpathian J. Math. 24, No. 1, 56--67 (2008; Zbl 1174.18301)