%0 Journal Article
%T Model Categories for Orthogonal Calculus
%A David Barnes
%A Peter Oman
%J Mathematics
%D 2011
%I arXiv
%R 10.2140/agt.2013.13.959
%X We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.
%U http://arxiv.org/abs/1101.4099v3