Homotopy theory of modules over operads in symmetric spectra

TL;DR

This paper develops a homotopy-theoretic framework for modules over operads in symmetric spectra, establishing model structures and conditions for Quillen equivalences between categories of algebras and modules.

Contribution

It introduces model category structures for algebras and modules over operads in symmetric spectra and analyzes when operad morphisms induce Quillen equivalences.

Findings

Model category structures are established for algebras and modules over operads.

Conditions for Quillen equivalences induced by operad morphisms are identified.

The framework advances the homotopy theory of modules over operads in symmetric spectra.

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.