  We show that there exists a Lie a bracket on the cohomology of any type of
(bi)algebras over an operad or a PROP, induced by a strongly homotopy Lie
structure on the defining cochain complex, such that the associated "quantum"
master equation captures deformations.
  This in particular implies the existence of a Lie bracket on the
Gerstenhaber-Schack cohomology of a bialgebra that extends the classical
intrinsic bracket on the Hochschild cohomology, giving an affirmative answer to
an old question about the existence of such a bracket.
