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Simplicial localisation of homotopy algebras over a prop

Published online by Cambridge University Press:  13 October 2014

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

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
Copyright
Copyright © Cambridge Philosophical Society 2014 

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