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On a Quillen adjunction between the categories of differential graded and simplicial coalgebras. (English) Zbl 1448.18037

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 ScoAlg, introduced by Goerss, and the model category of differential graded coalgebras DGcoAlg due to Getzler-Goerss. Then, this paper corrects [W. H. B. Sore, J. Homotopy Relat. Struct. 12, No. 2, 511–512 (2017; Zbl 1448.18036)] (see also [W. H. B. Sore, J. Homotopy Relat. Struct. 11, No. 1, 67–96 (2016; Zbl 1349.18031)]).

MSC:

18N40 Homotopical algebra, Quillen model categories, derivators
18N50 Simplicial sets, simplicial objects
16T15 Coalgebras and comodules; corings
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References:

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