(Infinity,2)-Categories and the Goodwillie Calculus I

TL;DR

This paper compares different models of (infinity,2)-categories, aiming to establish foundational tools for studying Goodwillie calculus of functors, with initial applications to derivatives.

Contribution

It introduces a comparison of models for (infinity,2)-categories and sets the groundwork for applying Goodwillie calculus to higher categories.

Findings

Comparison of models for (infinity,2)-categories

Foundations for Goodwillie calculus in higher categories

Initial applications to derivatives in functor calculus

Abstract

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 considered). Our ultimate goal is to lay the foundations for a study of Tom Goodwillie's calculus of functors. To this end, we have included some simple applications to the theory of first derivatives.