Reference : Simplicial localization of homotopy algebras over a prop
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Simplicial localization of homotopy algebras over a prop
Yalin, Sinan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathematical Proceedings of the Cambridge Philosophical Society
Cambridge University Press
Yes (verified by ORBilu)
[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.

File(s) associated to this reference

Fulltext file(s):

Open access
Simplicial localization of homotopy algebras over a prop.pdfPublisher postprint345.69 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.