Reference : Classifying spaces of algebras over a prop |

Scientific journals : Article | |||

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

http://hdl.handle.net/10993/22422 | |||

Classifying spaces of algebras over a prop | |

English | |

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

2014 | |

Algebraic and Geometric Topology | |

14 | |

5 | |

2561--2593 | |

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

International | |

1472-2747 | |

1472-2739 | |

[en] props ; classifying spaces ; moduli spaces ; bialgebras ; homotopical algebra ; homotopy invariance | |

[en] We prove that a weak equivalence between cofibrant props induces
a weak equivalence between the associated classifying spaces of algebras. This statement generalizes to the prop setting a homotopy invariance result which is well known in the case of algebras over operads. The absence of model category structure on algebras over a prop leads us to introduce new methods to overcome this difficulty. We also explain how our result can be extended to algebras over colored props in any symmetric monoidal model category tensored over chain complexes. | |

http://hdl.handle.net/10993/22422 |

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