Algebraic & Geometric Topology

Homotopy theory of non-symmetric operads, II: Change of base category and left properness

Fernando Muro

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We prove, under mild assumptions, that a Quillen equivalence between symmetric monoidal model categories gives rise to a Quillen equivalence between their model categories of (non-symmetric) operads, and also between model categories of algebras over operads. We also show left properness results on model categories of operads and algebras over operads. As an application, we prove homotopy invariance for (unital) associative operads.

Article information

Algebr. Geom. Topol., Volume 14, Number 1 (2014), 229-281.

Received: 24 April 2013
Revised: 9 August 2013
Accepted: 9 August 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18D50: Operads [See also 55P48] 55U35: Abstract and axiomatic homotopy theory
Secondary: 18G55: Homotopical algebra

operad algebra model category Quillen equivalence $A$–infinity algebra


Muro, Fernando. Homotopy theory of non-symmetric operads, II: Change of base category and left properness. Algebr. Geom. Topol. 14 (2014), no. 1, 229--281. doi:10.2140/agt.2014.14.229.

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