(also nonabelian homological algebra)
symmetric monoidal (∞,1)-category of spectra
The monoidal Dold-Kan correspondence relates algebras over an operad in abelian simplicial groups with algebras over an operad in chain complexes.
This generalizes the monoidal Dold-Kan correspondence.
In (Mandell) a Quillen equivalence between E-infinity algebras in chain complexes and in simplicial abelian groups is demonstrated.
In (Richter) it is shown that for any reduced operad $\tilde \mathcal{O}$ in $Ch_\bullet^+(Mod)$, which is a resolution of an operad in $Mod$, the inverse map $\Gamma : Ch_\bullet^+ \to sAb$ of the Dold-Kan correspondence lifts to a Quillen adjunction between homotopy $\mathcal{O}$-algebras in $Ch_\bullet(Mod)$ and in $Mod^{\Delta^{op}}$. (Around therem 5.5.5). It is not shown yet if or under which conditions this is a Quillen equivalence.
operadic Dold-Kan correspondence
A Quillen equivalence between $E_\infty$ dg-algebras and $E_\infty$ simplicial algebras is given in
where the Moore complex functor is the right adjoint.
A construction that allows its inverse to be part of the adjunction is in
Last revised on November 4, 2010 at 23:51:51. See the history of this page for a list of all contributions to it.