## Algebraic & Geometric Topology

### Classifying spaces of algebras over a prop

Sinan Yalin

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 2561-2593.

Dates
Revised: 19 December 2013
Accepted: 24 February 2014
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715996

Digital Object Identifier
doi:10.2140/agt.2014.14.2561

Mathematical Reviews number (MathSciNet)
MR3276841

Zentralblatt MATH identifier
1315.18025

#### Citation

Yalin, Sinan. Classifying spaces of algebras over a prop. Algebr. Geom. Topol. 14 (2014), no. 5, 2561--2593. doi:10.2140/agt.2014.14.2561. https://projecteuclid.org/euclid.agt/1513715996

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