Volume 14, issue 1 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
References
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