Liftings of normal functors in the category of compacta to categories of topological algebra and analysis (Q392735)

The authors study natural liftings of a normal functor \(F\) in the category of compact Hausdorff spaces to the categories of (abelian) compact semigroups (monoids). They show that they are determined by natural transformations \(F(-)\times F(-)\to F(-\times -)\) fulfilling conditions corresponding to associativity, commutativity, and the existence of a unity. The tensor products for normal monads satisfy (not necessarily all) these requirements. Furthermore the authors construct an example of a natural lifting for a normal functor not defined by the tensor product. Finally they establish that, for a normal functor, there exists a natural lifting to the category of convex compacta and continuous affine mappings if and only if the functor is a power functor.