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 …

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 …

We study the structure possessed by the Goodwillie derivatives of a pointed homotopy
functor of based topological spaces. These derivatives naturally form a bimodule over the …

We describe new structure on the Goodwillie derivatives of a functor, and we show how the
full Taylor tower of the functor can be recovered from this structure. This new structure takes …

We introduce various homotopy structures on the category of operads, which shed some
light into the homotopy theoretic nature of the barconstruction WB of an operad, the …

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 …

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 …

An operad is an abstraction of a family of composable functions of n variables for various n,
useful for the “bookkeeping” and applications of such families. Operads are particularly …

Operads may be represented as symmetric monoidal functors on a small symmetric
monoidal category. We discuss the axioms which must be imposed on a symmetric …

We establish that En-operads satisfy a rational intrinsic formality theorem for n≥ 3. We get
our results in the category of Hopf cooperads in cochain graded dg-modules which defines a …