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 mailto [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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