Simplicial localization of homotopy algebras over a prop

Sinan Yalin

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arXiv · 1307.4840

Simplicial localization of homotopy algebras over a prop

Sinan Yalin

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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 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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BibTeX RIS

Sinan Yalin. 2014-05-02. Simplicial localization of homotopy algebras over a prop. https://arxiv.org/abs/1307.4840

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