#### Volume 14, issue 1 (2014)

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

### Fernando Muro

Algebraic & Geometric Topology 14 (2014) 229–281
##### 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.

##### Keywords
operad, algebra, model category, Quillen equivalence, $A$–infinity algebra
##### Mathematical Subject Classification 2010
Primary: 18D50, 55U35
Secondary: 18G55
##### Publication
Received: 24 April 2013
Revised: 9 August 2013
Accepted: 9 August 2013
Preview posted: 5 December 2013
Published: 9 January 2014
##### Authors
 Fernando Muro Facultad de Matemáticas, Departamento de Álgebra Universidad de Sevilla Avda. Reina Mercedes s/n 41012 Sevilla Spain http://personal.us.es/fmuro