Homology, Homotopy and Applications
Volume 18 (2016)
Cocommutative coalgebras: homotopy theory and Koszul duality
Pages: 303 – 336
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.
coalgebra, curved Lie algebra, deformation, rational homotopy
2010 Mathematics Subject Classification
16T15, 17B55, 18G55, 55P62, 81R99