Title: Goodwillie's calculus and model categories
Author(s): Georg Biedermann, Boris Chorny, Oliver Roendigs
Author's e-mail address: gbiederm@uwo.ca, chorny@math.ethz.ch,
oroendig@math.uni-bielefeld.de
AMS classification number: 18G55 (primary); 55P65, 55P60 (secondary)
Other useful information (such as arXive submission number): math.AT/0601221
Abstract:
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 functors from simplicial sets to spectra. We
apply these model categories in the study of calculus of functors,
namely for classification of polynomial and homogeneous
functors. Finally we show that the $n$-th derivative induces a Quillen
map between the $n$-homogeneous model structure on small functors from
pointed simplicial sets to spectra and the category of spectra with
$\Sigma_n$-action. We consider also a finitary version of the
$n$-homogeneous model structure and the $n$-homogeneous model structure
on functors from pointed finite simplicial sets to spectra. In these two
cases the above Quillen map becomes a Quillen equivalence. This improves
the classification of finitary homogeneous functors by T. G. Goodwillie.