Article (Scientific journals)
Simplicial localization of homotopy algebras over a prop
Yalin, Sinan
2014In Mathematical Proceedings of the Cambridge Philosophical Society, 157 (3), p. 457–468
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Keywords :
props; bialgebras; simplicial localization; infinity-categories; homotopical algebra; homotopy invariance
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Yalin, Sinan ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Simplicial localization of homotopy algebras over a prop
Publication date :
2014
Journal title :
Mathematical Proceedings of the Cambridge Philosophical Society
ISSN :
1469-8064
Publisher :
Cambridge University Press
Volume :
157
Issue :
3
Pages :
457–468
Peer reviewed :
Peer Reviewed verified by ORBi
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