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Simplicial localisation of homotopy algebras over a prop

Published online by Cambridge University Press:  13 October 2014

SINAN YALIN
SINAN YALIN*
Affiliation:
Mathematics Research Unit, Luxembourg University, 6 Rue Richard Coudenhove–Kalergi, L-1359 Luxembourg.
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Abstract

We prove that a weak equivalence between two cofibrant (colored) props in chain complexes induces a Dwyer–Kan equivalence between the simplicial localisations 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 3 , November 2014 , pp. 457 - 468
Copyright
Copyright © Cambridge Philosophical Society 2014 

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