Cochains and homotopy type
Publications Mathématiques de l'IHÉS, Volume 103 (2006), pp. 213-246.

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

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