  The purpose of this paper is to study Sabinin algebras of Hom-type. It is
shown that Lie, Malcev, Bol and other algebras of Hom-type are naturally
Sabinin algebras of Hom-type. To this end, we provide a general key
construction that establish a relationship between identities of some class of
Hom-algebras and ordinary algebras. Moreover, we discuss a new concept of
Hom-bialgebra, in relation with universal enveloping Hom-algebras. A study
based on primitive elements is provided.
