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Aldridge Bousfield, Victor Gugenheim:
On PL deRham theory and rational homotopy type,
Memoirs of the AMS, vol. 179 (1976)
on rational homotopy theory via a model structure on dg-algebras (hence on objects dual to the dg-Lie algebras originally considered in Quillen 69).
Related references:
Review:
Kathryn Hess, Rational homotopy theory: a brief introduction, contribution to Summer School on Interactions between Homotopy Theory and Algebra, University of Chicago, July 26-August 6, 2004, Chicago (arXiv:math.AT/0604626), chapter in Luchezar Lavramov, Dan Christensen, William Dwyer, Michael Mandell, Brooke Shipley (eds.), Interactions between Homotopy Theory and Algebra, Contemporary Mathematics 436, AMS 2007 (doi:10.1090/conm/436)
Joshua Moerman, Rational Homotopy Theory, 2015 (pdf, pdf)
Generalization to equivariant rational homotopy theory (fundamental theorem of equivariant rational homotopy theory?):
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