Algebraic & Geometric Topology

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

Fernando Muro

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715800

Digital Object Identifier
doi:10.2140/agt.2014.14.229

Mathematical Reviews number (MathSciNet)
MR3158759

Zentralblatt MATH identifier
1281.18001

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

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

Citation

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. https://projecteuclid.org/euclid.agt/1513715800


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References

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