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 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 …

The orthogonal and unitary calculi give a method to study functors from the category of real
or complex inner product spaces to the category of based topological spaces. We construct …

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 …

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 …

In classical set theory, there are many equivalent ways to introduce ordinals. In a
constructive setting, however, the different notions split apart, with different advantages and …

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 …

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 …

This is a continuation, completion, and generalization of our previous joint work with Boris
Chorny [Adv. Math. 214 (2007) 92–115]. We supply model structures and Quillen …

Tangent categories provide an axiomatic framework for understanding various tangent
bundles and differential operations that occur in differential geometry, algebraic geometry …