Cochains and homotopy type

Mandell, Michael A.

Publications Mathématiques de l'IHÉS, Tome 103 (2006), pp. 213-246.

Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as $E_{\infty }$ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of $E_{\infty }$ algebras is faithful but not full.

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