### Congruences and homomorphisms on $\Omega $-algebras

The topic of the paper are $\Omega $-algebras, where $\Omega $ is a complete lattice. In this research we deal with congruences and homomorphisms. An $\Omega $-algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an $\Omega $-valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce $\Omega $-valued congruences, corresponding quotient $\Omega $-algebras and $\Omega $-homomorphisms and we investigate connections among these notions. We prove...