Cocommutative algebras : homotopy theory and Koszul duality

Chuang, Joseph and Lazarev, Andrey and Mannan, Wajid Hassan (2016) Cocommutative algebras : homotopy theory and Koszul duality. Homology, Homotopy and Applications, 18 (2). pp. 303-336. ISSN 1532-0073

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Abstract

We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero. We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative coalgebras and formal coproducts of curved Lie algebras.