We show that topological Quillen homology of algebras and modules over operads in
symmetric spectra can be calculated by realizations of simplicial bar constructions. Working …

Homotopy theory of modules over operadsin symmetric spectra Page 1 Algebraic & Geometric
Topology 9 (2009) 1637–1680 1637 Homotopy theory of modules over operads in symmetric …

Working in the context of symmetric spectra, we describe and study a homotopy completion
tower for algebras and left modules over operads in the category of modules over a …

We provide general conditions under which the algebras for a coloured operad in a
monoidal model category carry a Quillen model structure, and prove a Comparison Theorem …

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 …

We describe a cooperad structure on the simplicial bar construction on a reduced operad of
based spaces or spectra and, dually, an operad structure on the cobar construction on a …

A modern insight due to Quillen, which is further developed by Lurie, asserts that many
cohomology theories of interest are particular cases of a single construction, which allows …

We give sufficient conditions for homotopical localization functors to preserve algebras over
coloured operads in monoidal model categories. Our approach encompasses a number of …

In this paper we study spaces of algebras over an operad (nonsymmetric) in symmetric
monoidal model categories. We first compute the homotopy fiber of the forgetful functor …

Let 𝒱 be a cofibrantly generated monoidal model category and ℳ be a monoidal 𝒱‐model
category. If C is any set, then we denote by ℳC the product category of copies of ℳ indexed …