On rational homotopy theory, the fundamental theorem of dg-algebraic rational homotopy theory and its generalization both to Borel-equivariant rational homotopy theory (for covering spaces of non-nilpotent spaces) and to real homotopy theory (using continuous real cohomology and topological dgc-algebras):
based on (including discussion of globally Kan fibrant topological simplicial groups):
Edgar H. Brown, Robert H. Szczarba, Continuous cohomology and real homotopy type, Trans. Amer. Math. Soc. 311 (1989), no. 1, 57 (doi:10.1090/S0002-9947-1989-0929667-6, jstor:2001017)
Edgar Brown, Robert H. Szczarba, Continuous cohomology and Real homotopy type II Asterisque 191, Societe Mathematique De France (1990) (numdam:AST_1990__191__45_0)
Edgar Brown, Robert H. Szczarba, Real and rational homotopy theory for spaces with arbitrary fundamental group, Duke Mathematical Journal 71. (1993): 229-316 (doi:10.1215/S0012-7094-93-07111-6)
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