Classes of analytic functions related to Blaschke products

Basing on the well known Riesz Theorem on the canonical factorization of bounded analytic functions, we distinguished the subfamilies of the Carath?odory class of functions. The basic properties of introduced classes have been proved. Related classes of analytic functions are discussed also.

Weak Homomorphisms of Coalgebras Beyond Set

We study the notion of weak homomorphisms between coalgebras of different types generalizing thereby that of homomorphisms for similarly typed coalgebras. This helps extend some results known so far in the theory of Universal coalgebra over Set. We find conditions under which coalgebras of a set of types and weak homomorphisms between them form a category. Moreover, we establish an Isomorphism Theorem that extends the so-called First Isomorphism Theorem, showing thereby that this category admits a canonical factorization structure for morphisms