Geodesic
Cochains and homotopy type
Publications Mathématiques de l'IHÉS, Tome 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.

Mandell, Michael A. Cochains and homotopy type. Publications Mathématiques de l'IHÉS, Tome 103 (2006), pp. 213-246. doi: 10.1007/s10240-006-0037-6
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     title = {Cochains and homotopy type},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {213--246},
     year = {2006},
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     zbl = {1105.55003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-006-0037-6/}
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