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Cochains and homotopy type
Publications Mathématiques de l'IHÉS, Volume 103 (2006), pp. 213-246
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Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E ∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E ∞ algebras is faithful but not full.

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DOI: 10.1007/s10240-006-0037-6 
Michael A. Mandell. Cochains and homotopy type. Publications Mathématiques de l'IHÉS, Volume 103 (2006), pp. 213-246. doi: 10.1007/s10240-006-0037-6
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