Homotopy theory of modules over operads in symmetric spectra

2008/01/31 by John E. Harper, John E Harper · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Equivalence (formal languages) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Model category #Morphism #Spectral line #math.AT #msc:55P43 #msc:55P48 #msc:55U35

paper · pdf · doi:10.2140/agt.2009.9.1637

published as Algebr. Geom. Topol. 9 (2009) 1637-1680 · Corrigendum

openalex publication_date 2009/08/22 · arxiv created 2014/05/15 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We establish model category structures on algebras and modules over operads in symmetric spectra and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads.

Citations

• Homotopy Theories and Model Categories
• Homology and cohomology of E? ring spectra
• Modules in monoidal model categories
• The Geometry of Iterated Loop Spaces
• Koszul duality for operads
• Homotopical Algebra
• Simplicial Homotopy Theory

Cited by

• Bar constructions and Quillen homology of modules over operads