  The codomain category of a generalized homology theory is the category of
modules over a ring. For an abelian category A, an A-valued (generalized)
homology theory is defined by formally replacing the category of modules with
the category A. It is known that the category of bicommutative (i.e.
commutative and cocommutative) Hopf algebras over a field k is an abelian
category. Denote the category by H. In this paper, we give some ways to
construct H-valued homology theories. As a main result, we give H-valued
homology theories whose coefficients are neither group Hopf algebras nor
function Hopf algebras. The examples contain not only ordinary homology
theories but also extraordinary ones.
