Reference : Simplicial localization of homotopy algebras over a prop |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/22423 | |||

Simplicial localization of homotopy algebras over a prop | |

English | |

Yalin, Sinan [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

2014 | |

Mathematical Proceedings of the Cambridge Philosophical Society | |

Cambridge University Press | |

157 | |

3 | |

457–468 | |

Yes (verified by ORBi^{lu}) | |

International | |

0305-0041 | |

1469-8064 | |

[en] props ; bialgebras ; simplicial localization ; infinity-categories ; homotopical algebra ; homotopy invariance | |

[en] We prove that a weak equivalence between two cofibrant (colored)
props in chain complexes induces a Dwyer-Kan equivalence between the simplicial localizations of the associated categories of algebras. This homotopy invariance under base change implies that the homotopy category of homotopy algebras over a prop P does not depend on the choice of a cofibrant resolution of P, and gives thus a coherence to the notion of algebra up to homotopy in this setting. The result is established more generally for algebras in combinatorial monoidal dg categories. | |

http://hdl.handle.net/10993/22423 |

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