Mentioned by James Griffin
[arXiv:1109.3715]http://front.math.ucdavis.edu/1109.3715) Maurer-Cartan moduli and models for function spaces from arXiv Front: math.AT by Andrey Lazarev We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential graded coalgebras). Among other things this formalism allows us to give a compact and manifestly homotopy invariant treatment of Chevalley-Eilenberg and Harrison cohomology. We apply the developed technology to construct rational homotopy models for function spaces.
http://mathoverflow.net/questions/6175/cohomology-of-associative-algebras
nLab page on Harrison cohomology