The lazy homology of a Hopf algebra

To any Hopf algebra H we associate two commutative Hopf algebras and , which we call the lazy homology Hopf algebras of H. These Hopf algebras are built in such a way that they are “predual” to the lazy cohomology groups based on the so-called lazy cocycles. We establish two universal coefficient theorems relating the lazy cohomology to the lazy homology and we compute the lazy homology of the Sweedler algebra.