On covariant functors in the category of compact Hausdorff spaces

We investigate covariant functors in the category of compact Hausdorff spaces and obtain 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 same degree. Under CH, a compact discretely generated space Z is constructed such that F(Z) is not discretely generated for any seminormal functor F of finite degree.