Понятие клеточного подфунктора ковариантного функтора в категории COMP

It has introduced the concept of cellular subfunctor in the category COMP of all compact spaces and their mappings. We has proved that the space of all nonempty closed subsets of $X$ is cellular embed to the $\lambda(X\cup \{p\})$. One of the general results proved in this article is the equality $c(F(X))=c(X^{\omega})$ for covariant functors $\mathcal{N}^k, \lambda$ and $G$.