Cochains and homotopy type
Publications Mathématiques de l'IHÉS, Volume 103  (2006), p. 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.

@article{PMIHES_2006__103__213_0,
     author = {Mandell, Michael A.},
     title = {Cochains and homotopy type},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer},
     volume = {103},
     year = {2006},
     pages = {213-246},
     doi = {10.1007/s10240-006-0037-6},
     zbl = {1105.55003},
     mrnumber = {2233853},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2006__103__213_0}
}
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/item/PMIHES_2006__103__213_0/

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