| 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 ORBilu) | |
| 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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