Cocommutative coalgebras: homotopy theory and Koszul duality (Q505365)

Let \(k\) be an algebraically closed field of characteristic 0. The authors construct a closed model category (shortly CMC) structure on the category \(\mathcal{V}\) of cocommutative differential graded coalgebras over \(k\). This extends a construction of \textit{V. Hinich} [J. Pure Appl. Algebra 162, No. 2--3, 209--250 (2001; Zbl 1020.18007)]. It is proved that the category of formal (co)products of objects in a CMC is also a CMC. The category of curved Lie algebras is showed to be a CMC, and it is proved that \(\mathcal{V}\) is Quillen equivalent to the category of formal coproducts of curved Lie algebras.