Cocommutative coalgebras: homotopy theory and Koszul duality

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.

38 pages

References in corpus (2)

• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
• Cofree coalgebras over operads II Homology invariance

Cited by in corpus (6)

• Double field theory algebroid and curved $L_{\infty }$-algebras
• Koszul duality and homotopy theory of curved Lie algebras
• Relative nonhomogeneous Koszul duality
• Homotopy theory of unital algebras
• Curved Koszul duality of algebras over unital versions of binary operads
• Unbased rational homotopy theory: a Lie algebra approach