Capturing Goodwillie's Derivative
Abstract
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 focus on understanding the derivative as a right Quillen functor to a new model category. This is directly analogous to the behaviour of Weiss's derivative in orthogonal calculus. The immediate advantage of this new category is that we obtain a streamlined and more informative proof that the n-homogeneous functors are classified by spectra with an action of the symmetric group on n objects. In a later paper we will use this new model category to give a formal comparison between the orthogonal calculus and Goodwillie's calculus of functors.
Cite
@article{arxiv.1406.0424,
title = {Capturing Goodwillie's Derivative},
author = {David Barnes and Rosona Eldred},
journal= {arXiv preprint arXiv:1406.0424},
year = {2015}
}
Comments
Final version, to appear. Substantially shortened from earlier version, with a significantly expanded introduction, new results and examples. 27 pages