  We prove that a finite-dimensional Hopf algebra with the dual Chevalley
Property over a field of characteristic zero is quasi-isomorphic to a
Radford-Majid bosonization whenever the third Hochschild cohomology group in
the category of Yetter-Drinfeld modules of its diagram with coefficients in the
base field vanishes. Moreover we show that this vanishing occurs in meaningful
examples where the diagram is a Nichols algebra.
