operadic Dold-Kan correspondence
Algebras and modules
Model category presentations
Geometry on formal duals of algebras
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 in , which is a resolution of an operad in , the inverse map of the Dold-Kan correspondence lifts to a Quillen adjunction between homotopy -algebras in and in . (Around therem 5.5.5). It is not shown yet if or under which conditions this is a Quillen equivalence.
A Quillen equivalence between dg-algebras and simplicial algebras is given in
- Michael Mandell, Topological André-Quillen Cohomology and André-Quillen Cohomology Adv. in Math., Adv. Math. 177 (2) (2003) 227–279
where the Moore complex functor is the right adjoint.
A construction that allows its inverse to be part of the adjunction is in
- Birgit Richter, Homotopy algebras and the inverse of the normalization functor (pdf) .
Revised on November 4, 2010 23:51:51
by Urs Schreiber