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 ![]() | |
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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