Related papers: Goodwillie approximations to higher categories
Building on work of Marta Bunge in the one-categorical case, we characterize when a given model category is Quillen equivalent to a presheaf category with the projective model structure. This involves introducing a notion of homotopy atoms,…
For a complete and cocomplete category $\mathcal{C}$ with a well-behaved class of `projectives' $\bar{\mathcal{P}}$, we construct a model structure on the category $s\mathcal{C}$ of simplicial objects in $\mathcal{C}$ where the weak…
We construct the unitary analogue of orthogonal calculus developed by Weiss, utilising model categories to give a clear description of the intricacies in the equivariance and homotopy theory involved. The subtle differences between real and…
For a homological functor from a triangulated category to an abelian category satisfying some technical assumptions we construct a tower of interpolation categories. These are categories over which the functor factorizes and which capture…
We describe Taylor towers for spaces of knots arising from Goodwillie-Weiss calculus of the embedding functor and extend the configuration space integrals of Bott and Taubes from spaces of knots to the stages of the towers. We show that…
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 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…
In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between the categories of simplicial sets and complete differential…
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…
We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is "pieced together" from the G/U-homotopy theories…
We survey the theory and applications of Goodwillie's calculus of homotopy functors and related topics.
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…
The settings for homotopical algebra---categories such as simplicial groups, simplicial rings, $A_\infty$ spaces, $E_\infty$ ring spectra, etc.---are often equivalent to categories of algebras over some monad or triple $T$. In such cases,…
We study Goodwillie-Weiss embedding calculus through its relationship with Goodwillie's functor calculus. Specifically, building on a result of Tillmann and Weiss, we construct a functorial complement for \(T_{n}\)-embeddings that takes…
We develop a generalization of manifold calculus in the sense of Goodwillie-Weiss where the manifold is replaced by a simplicial complex. We consider functors from the category of open subsets of a fixed simplical complex into the category…
Let G be a compact Lie group. We build a tower of G-spectra over the suspension spectrum of the space of linear isometries from one G-representation to another. The stable cofibres of the maps running down the tower are certain interesting…
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…
The purpose of this paper is to explain why the functor that sends a stratified topological space $S$ to the $\infty$-category of constructible (hyper)sheaves on $S$ with coefficients in a large class of presentable $\infty$categories is…
In this paper, we show that for reduced homotopy endofunctors of spaces, F, and for all $n \geq 1$ there are adjoint functors $R_n, L_n$ with $T_n F \simeq R_n F L_n$, where $P_n F$ is the $n$-excisive approximation to $F$, constructed by…
Recently, the Johnson-McCarthy discrete calculus for homotopy functors was extended to include functors from an unbased simplicial model category to spectra. This paper completes the constructions needed to ensure that there exists a…