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 …

In this paper, we consider abelian functor calculus, the calculus of functors of abelian
categories established by the second author and McCarthy. We carefully construct a …

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 formulate and prove a chain rule for the derivative, in the sense of Goodwillie, of
compositions of weak homotopy functors from simplicial sets to simplicial sets. The …

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 …

A generalized Grothendieck spectral sequence Page 171 A generalized Grothendieck spectral
sequence David Blanc Northwestern University Christopher Stover University of Chicago June …

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 …

The purpose of this foundational paper is to introduce various notions and constructions in
order to develop the homotopy theory for differential graded operads over any ring. The …

Manifold calculus is a form of functor calculus concerned with functors from some category of
manifolds to spaces. A weakness in the original formulation is that it is not continuous in the …