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

Muro, Fernando

doi:10.2140/agt.2014.14.229

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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

DOI: 10.2140/agt.2014.14.229

Correction: 10.2140/agt.2017.17.3837

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

Correction: 4 October 2017

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

Volume 14, issue 1 (2014)