## Abstract

Let A be a DGA over a field and X a module over H_{*} (A). Fix an A_{∞}-structure on H_{*} (A) making it quasi-isomorphic to A. We construct an equivalence of categories between A_{n + 1}-module structures on X and length n Postnikov systems in the derived category of A-modules based on the bar resolution of X. This implies that quasi-isomorphism classes of A_{n}-structures on X are in bijective correspondence with weak equivalence classes of rigidifications of the first n terms of the bar resolution of X to a complex of A-modules. The above equivalences of categories are compatible for different values of n. This implies that two obstruction theories for realizing X as the homology of an A-module coincide.

Original language | English |
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Pages (from-to) | 1394-1414 |

Number of pages | 21 |

Journal | Journal of Pure and Applied Algebra |

Volume | 212 |

Issue number | 6 |

DOIs | |

State | Published - 1 Jan 2008 |

Externally published | Yes |

## ASJC Scopus subject areas

- Algebra and Number Theory