  Covariant Hom-bimodules are introduced and the structure theory of them in
the Hom-setting is studied in a detailed way. The category of bicovariant
Hom-bimodules is proved to be a (pre)braided monoidal category and its
structure theory is also provided in coordinate form. The notion of
Hom-Yetter-Drinfel'd modules is presented and it is shown that the category of
Hom-Yetter-Drinfel'd modules is a (pre)braided tensor category as well. As one
of the main results, a (pre)braided monoidal equivalence between these tensor
categories is verified, which extends the fundamental theorem of Hom-Hopf
modules.
