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

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.

43 pages. Minor changes: a couple of remarks, corollaries and references have been added

References in corpus (4)

• Higher Topos Theory
• Homotopy theory of non-symmetric operads
• Homotopy units in A-infinity algebras
• Unital $A_{\infty }$-categories

Cited by in corpus (3)

• Admissibility and rectification of colored symmetric operads
• Corrections to "Homotopy theory of nonsymmetric operads, I, II"
• Moduli spaces of algebras over non-symmetric operads