On covariant functors in the category of compact Hausdorff spaces (Q465853)

This article investigates covariant functors in the category of compact Hausdorff spaces, and obtains a series of results allowing to construct normal and seminormal functors of finite degree with desired properties. In particular, it turns out that any functor of finite degree is a factor-functor of some monomorphic functor of the some degree. Under \(CH\), a compact discretely generated space \(Z\) is constructed such that \(F\left( Z \right)\) is not discretely generated for any seminormal functor \(F\) of finite degree.