Right Modules over Operads and Functors

Benoit Fresse Modules over Operads and Functors

Calculus of Functors and Configuration Spaces

This is a summary of a talk given at the Conference on Pure and Applied Topology on the Isle of Skye from June 21-25, 2005. The author would like to thank the organisers of the conference for a fantastic week and for the opportunity to present the following work. We describe a relationship between Goodwillie’s calculus of homotopy functors and configuration spaces. In [3], we showed that the Go...

On Triples, Operads, and Generalized Homogeneous Functors

We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors F : A → MA from a pointed category with coproducts to A-modules in terms of differentials of F . Here A is a commutative S-algebra. We specialize to the case when A is the category of a-algebras for an operad a and F is the forgetful functor, and derive mild...

Localization of Algebras over Coloured Operads

We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under localizations, such as loop spaces or infinite loop spaces, and provides new results of the same kind. For instance, under suitable assumptions, homotopical locali...

Functor Calculus and Operads

Speaker: Gregory Arone (Virginia) Title: Part 1: operads, modules and the chain rule Abstract: Let F be a homotopy functor between the categories of pointed topological spaces or spectra. By the work of Goodwillie, the derivatives of F form a symmetric sequence of spectra ∂∗F . This symmetric sequence determines the homogeneous layers in the Taylor tower of F , but not the extensions in the tow...