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arXiv · 1309.2820

Brace Bar-Cobar Duality

Justin Young
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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.

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Justin Young. 2013-09-12. Brace Bar-Cobar Duality. https://arxiv.org/abs/1309.2820

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