Related papers: Goodwillie calculus and Mackey functors

We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categories of multivariable excisive functors from spectra to…

We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial G-sets to symmetric G-spectra, where G is a finite group. We extend a notion of G-linearity suggested by Blumberg to define stably excisive and…

In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving $d$-excisive functors from pointed spaces to spectra as spectrum-valued functors on the category of finite sets of…

We develop and extend the theory of Mackey functors as an application of enriched category theory. We define Mackey functors on a lextensive category $\E$ and investigate the properties of the category of Mackey functors on $\E$. We show…

Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as defined by Dress. We show that they can be described as excisive functors on a suitable infinity-category, and we use this to show that universal…

The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is also…

Let $G$ be a finite group. In this paper, we first introduce a new notion, so-called the Mackey double category of $G$. Then we prove that the category of Mackey double categories and the category of Mackey functors of $G$ are equivalent.

We develop a theory of Goodwillie calculus for functors between $G$-equivariant homotopy theories, where $G$ is a finite group. We construct $J$-excisive approximations of a homotopy functor for any finite $G$-set $J$. These fit together…

We give a functorial construction of equivariant spectra from a generalized version of Mackey functors in categories. This construction relies on the recent description of the category of equivariant spectra due to Guillou and May. The key…

A Mackey type decomposition for group actions on abelian categories is described. This allows us to define new Mackey functors which associates to any subgroup the $K$-theory of the corresponding equivariantized abelian category. In the…

We make precise the analogy between Goodwillie's calculus of functors in homotopy theory and the differential calculus of smooth manifolds by introducing a higher-categorical framework of which both theories are examples. That framework is…

We develop an approach to Goodwillie's calculus of functors using the techniques of higher topos theory. Central to our method is the introduction of the notion of fiberwise orthogonality, a strengthening of ordinary orthogonality which…

Recent work of Biedermann and R\"ondigs has translated Goodwillie's calculus of functors into the language of model categories. Their work focuses on symmetric multilinear functors and the derivative appears only briefly. In this paper we…

In this paper we introduce the notion of a categorical Mackey functor. This categorical notion allows us to obtain new Mackey functors by passing to Quillen's $K$-theory of the corresponding abelian categories. In the case of an action by…

We study the category of polynomial functors from finitely generated free groups to a stable infinity-category D. We show that this category is equivalent to the category of excisive functors from pointed animas to D, and also to truncated…

We prove a thick subcategory theorem for the category of $d$-excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=1$ case) and the $C_2$-equivariant thick subcategory theorem…

This paper reformulates Goodwillie calculus of $\infty$-categories including non-presentable $\infty$-categories. In the case of presentable $\infty$-categories our definition is equivalent to Heuts's~\cite{Heuts2018} work. As an…

For any finite group G, we define a bivariant functor from the Dress category of finite G-sets to the conjugation biset category, whose objects are subgroups of G, and whose morphisms are generated by certain bifree bisets. Any additive…

The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure. In this paper we construct various localizations of the projective model structure and also give a variant for…

We present an introduction to the manifold calculus of functors, due to Goodwillie and Weiss. Our perspective focuses on the role the derivatives of a functor F play in this theory, and the analogies with ordinary calculus. We survey the…