Brace Bar-Cobar Duality

Abstract

Using Kadeishvili's formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras Ω: CoAlg -> Alg can be enhanced to a functor from Hopf algebras to E_2 algebras (for a certain choice of E_2 operad) Ω: 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.

21 pages, added contact information

References in corpus (1)

• The universal Hopf operads of the bar construction

Cited by in corpus (2)

• Quantisation of derived Lagrangians
• A Cacti theoretical interpretation of the axioms of bialgebras and H-module algebras