  To any Hopf algebra H we associate two commutative Hopf algebras, which we
call the first and second lazy homology Hopf algebras of H. These algebras are
related to the lazy cohomology groups based on the so-called lazy cocycles of H
by universal coefficient theorems. When H is a group algebra, then its lazy
homology can be expressed in terms of the 1- and 2-homology of the group. When
H is a cosemisimple Hopf algebra over an algebraically closed field of
characteristic zero, then its first lazy homology is the Hopf algebra of the
universal abelian grading group of the category of corepresentations of H. We
also compute the lazy homology of the Sweedler algebra.
