Homology, Homotopy and Applications

Volume 18 (2016)

Number 2

Cocommutative coalgebras: homotopy theory and Koszul duality

Pages: 303 – 336

DOI: https://dx.doi.org/10.4310/HHA.2016.v18.n2.a17


Joseph Chuang (Department of Mathematics, City University London, United Kingdom)

Andrey Lazarev (Department of Mathematics, University of Lancaster, United Kingdom)

W. H. Mannan (School of Mathematical Sciences, Queen Mary University of London, United Kingdom)


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

Published 29 November 2016