Weak Homomorphisms of Coalgebras Beyond Set

Abstract

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

Keywords

• and phrases: category
• functor
• coalgebraically equivalent coalgebras
• weak homomorphism
• closed strong subobject