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

Muro, Fernando¹

¹Facultad de Matemáticas, Departamento de Álgebra, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain

Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 229-281

Résumé

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.

Détail

DOI : 10.2140/agt.2014.14.229

Classification : 18D50, 55U35, 18G55
Keywords: operad, algebra, model category, Quillen equivalence, $A$–infinity algebra

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