Classifying spaces of algebras over a prop

Yalin, Sinan

doi:10.2140/agt.2014.14.2561

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Classifying spaces of algebras over a prop

Sinan Yalin

Algebraic & Geometric Topology 14 (2014) 2561–2593

DOI: 10.2140/agt.2014.14.2561

Abstract

We prove that a weak equivalence between cofibrant props induces a weak equivalence between the associated classifying spaces of algebras. This statement generalizes to the prop setting a homotopy invariance result which is well known in the case of algebras over operads. The absence of model category structure on algebras over a prop creates difficulties and we introduce new methods to overcome them. We also explain how our result can be extended to algebras over colored props in any symmetric monoidal model category tensored over chain complexes.

Keywords

props, classifying spaces, moduli spaces, bialgebras category, homotopical algebra, homotopy invariance

Mathematical Subject Classification 2010

Primary: 18G55

Secondary: 18D10, 18D50

References

Publication

Received: 9 October 2012

Revised: 19 December 2013

Accepted: 24 February 2014

Published: 5 November 2014

Authors

Sinan Yalin
Laboratoire Paul Painlevé Université de Lille 1 Cité Scientifique 59655 Villeneuve d’Ascq Cedex France

Volume 14, issue 5 (2014)