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 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 …

Let F be a homotopy functor with values in the category of spectra. We show that partially
stabilized cross-effects of F have an action of a certain operad. For functors from based …

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 …

In this article, we give precise mathematical form to the idea of a structure whose data and
axioms are faithfully represented by a graphical calculus; some prominent examples are …

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 give a new construction for the n-th Taylor polynomial, in the sense of Goodwillie
calculus, for homotopy functors from spectra to spectra. We then use this model to classify n …

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 …

Goodwillie's homotopy functor calculus constructs a Taylor tower of approximations to F,
often a functor from spaces to spaces. Weiss's orthogonal calculus provides a Taylor tower …

We use Lurie's symmetric monoidal envelope functor to give two new descriptions of∞-
operads: as certain symmetric monoidal∞-categories whose underlying symmetric …