  From the definition and properties of unital hom-associative algebras, and
the use of the Kaplansky's constructions, we develop new algebraic structures
called 2-hom-associative bialgebras, 2-hom-bialgebras, and 2-2-hom-bialgebras.
Besides, we devise a construction of hom-left symmetric dialgebras and discuss
their main relevant properties.
