  Using Kadeishvili's formulas with appropriate signs, we show that the
classical cobar construction from coalgebras to algebras \Omega: CoAlg -> Alg
can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain
choice of E_2 operad) \Omega : HopfAlg -> E_2 Alg, which, unlike its classical
counterpart, is not strictly adjoint, but homotopically equivalent to the left
adjoint of the enhanced bar construction B: E_2 Alg -> HopfAlg studied by
Gerstenhaber--Voronov and Fresse.
