Brace Bar-Cobar Duality

Publication date: 11 September 2013

Abstract: 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.

Mathematics Subject Classification ID

Chain complexes (category-theoretic aspects), dg categories (18G35) Chain complexes in algebraic topology (55U15) Hopf algebras and their applications (16T05) Duality in applied homological algebra and category theory (aspects of algebraic topology) (55U30)

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