On a Quillen adjunction between the categories of differential graded and simplicial coalgebras (Q2631917)

The author proves that the normalization functor of the Dold-Kan correspondence does not induce a Quillen equivalence between the model category of simplicial coalgebras \textbf{ScoAlg}, introduced by Goerss, and the model category of differential graded coalgebras \textbf{DGcoAlg} due to Getzler-Goerss. Then, this paper corrects [\textit{W. H. B. Sore}, J. Homotopy Relat. Struct. 12, No. 2, 511--512 (2017; Zbl 1448.18036)] (see also [\textit{W. H. B. Sore}, J. Homotopy Relat. Struct. 11, No. 1, 67--96 (2016; Zbl 1349.18031)]).