#### Volume 11, issue 3 (2011)

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Homotopy theory of nonsymmetric operads

### Fernando Muro

Algebraic & Geometric Topology 11 (2011) 1541–1599
##### Abstract

We endow categories of nonsymmetric operads with natural model structures. We work with no restriction on our operads and only assume the usual hypotheses for model categories with a symmetric monoidal structure. We also study categories of algebras over these operads in enriched nonsymmetric monoidal model categories.

##### Keywords
operad, algebra, model category, enriched $A_{\infty}$–category
##### Mathematical Subject Classification 2010
Primary: 18D50, 55U35
Secondary: 18D10, 18D35, 18D20
##### Publication
Received: 14 January 2011
Accepted: 19 February 2011
Published: 26 May 2011
##### 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