  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 a classification of polynomial
and homogeneous functors. In the $n$-homogeneous model structure, the $n$-th
derivative is a Quillen functor to the category of spectra with
$\Sigma_n$-action. After taking into account only finitary functors -- which
may be done in two different ways -- the above Quillen map becomes a Quillen
equivalence. This improves the classification of finitary homogeneous functors
by T. G. Goodwillie.
