Brace Bar-Cobar Duality
Abstract
Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras : CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E2 algebras (for a certain choice of E2 operad) : HopfAlg -> E2 Alg, which, unlike its classical counterpart, is not strictly adjoint, but homotopically equivalent to the left adjoint of the enhanced bar construction B: E2 Alg -> HopfAlg studied by Gerstenhaber--Voronov and Fresse.
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