Categorical and Cardinal Properties of Hyperspaces with a Finite Number of Components

In this paper, we examine categorical and cardinal properties of hyperspaces with finite number of components. We prove that the functor $C_{n}:\operatorname{Comp} \to \operatorname{Comp}$ is not normal, i.e., it does not preserve epimorphisms of continuous mappings. We also discuss the density, the caliber, and the Shanin number of the space $C_{n}(X)$.