The categories of \(A_{\infty}\) and \(E_{\infty}\)-monoids and ring spaces as closed simplicial and topological model categories
The authors deduce, by means of \textit{D. G. Quillen}'s [Homotopical algebra, (Lect. Notes Math. 43) (1967; Zbl 0168.209)] and \textit{W. G. Dwyer} and \textit{D. M. Kan}'s [Indag. Math. 46, 147-153 (1984; Zbl 0555.55019)] results, a closed topological model category structure on the category of \(\theta\)-spaces [\textit{J. M. Boardman} and \textit{R. M. Vogt}, Homotopy invariant algebraic structures on topological spaces (Lect. Notes Math. 347) (1973; Zbl 0285.55012)]. Then, closed simplicial and topological model category structures on the categories of \(A_{\infty}\)- resp. \(E_{\infty}\)-monoids or ring spaces are obtained.
\(A_{\infty }\)- resp. \(E_{\infty }\)-monoids
scientific article; zbMATH DE number 4213007
scientific article