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.
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