Abstract
We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of –equivariance clearer. Thus we develop model structures for the category of –polynomial and –homogeneous functors, along with Quillen pairs relating them. We then classify –homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an –action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.
Citation
David Barnes. Peter Oman. "Model categories for orthogonal calculus." Algebr. Geom. Topol. 13 (2) 959 - 999, 2013. https://doi.org/10.2140/agt.2013.13.959
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