相关论文: Cross-effects and the classification of Taylor tow…

The Taylor tower of a functor from based spaces to spectra can be classified according to the action of a certain comonad on the collection of derivatives of the functor. We describe various equivalent conditions under which this action can…

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 the form of a coalgebra over a certain comonad which…

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 operad consisting of the derivatives of the identity functor. We…

We study functors F from C_f to D where C and D are simplicial model categories and C_f is the full subcategory of C consisting of objects that factor a fixed morphism f from A to B. We define the analogs of Eilenberg and Mac Lane's cross…

We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors $F: \A \to M_A$ from a pointed category with coproducts to $A$-modules in terms of differentials of…

Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…

The aim of this paper is to study convergence of Bousfield-Kan completions with respect to the 1-excisive approximation of the identity functor and exotic convergence of the Taylor tower of the identity functor, for algebras over operads in…

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 cooperad. We also show that if the homology of the original…

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 for functors from vector spaces to spaces. In particular,…

Goodwillie's calculus of homotopy functors associates a tower of polynomial approximations, the Taylor tower, to a functor of topological spaces over a fixed space. We define a new tower, the varying center tower, for functors of categories…

We prove two theorems about Goodwillie calculus and use those theorems to describe new models for Goodwillie derivatives of functors between pointed compactly-generated infinity-categories. The first theorem say that the construction of…

We prove that the Goodwillie tower of a weak equivalence preserving functor from spaces to spectra can be expressed in terms of the tower for stable mapping spaces. Our proof is motivated by interpreting the functors P_n and D_n as…

We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More…

The aim of this paper is three-fold: (i) we construct a naturally occurring highly homotopy coherent operad structure on the derivatives of the identity functor on structured ring spectra which can be described as algebras over an operad…

We introduce a version of Koszul duality for categories, which extends the Koszul duality of operads and right modules. We demonstrate that the derivatives which appear in Weiss calculus (with values in spectra) form a right module over the…

We call attention to the intermediate constructions $\T_n F$ in Goodwillie's Calculus of homotopy functors, giving a new model which naturally gives rise to a family of towers filtering the Taylor Tower of a functor. We also establish a…

We define an ``algebraic'' version of the Goodwillie tower, P_n^alg F(X), that depends only on the behavior of F on coproducts of X. When F is a functor to connected spaces or grouplike H-spaces, the functor P_n^alg F is the base of a…

In this paper we study a category of trees TI and prove that it is a Koszul category. Consequences are the interpretation of the reduced bar construction of operads of Ginzburg and Kapranov as the Koszul complex of this category, and the…

This is a (slightly edited) version of the PhD dissertation of the author, submitted to Brown University in July 2005. We construct a homotopy calculus of functors in the sense of Goodwillie for the categories of rational homotopy theory.…

Let $\mathit{s}\mathcal{L}$ be the $\infty$-category of simplicial restricted Lie algebras over $\mathbf{F} = \overline{\mathbf{F}}_p$, the algebraic closure of a finite field $\mathbf{F}_p$. By the work of A. K. Bousfield et al. on the…