TY - EJOUR
AB - 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.
T1 - Brace Bar-Cobar Duality
DA - 2013
AU - Young, Justin Robert
JF - Documenta Mathematica : Journal der deutschen Mathematiker-Vereinigung
ID - 188727
SN - 1431-0635
UR - http://infoscience.epfl.ch/record/188727/files/bbcd%20paper.pdf
ER -