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Model categories for orthogonal calculus. (English) Zbl 1268.55001
Orthogonal calculus is a technique, similar to Goodwillie’s calculus, that captures homotopical properties of functors that take finite dimensional real vector spaces with inner product to pointed topological spaces.
In this paper the authors put the study of orthogonal calculus into the powerful language of model categories. Concretely, they develop polynomial and homogeneous model structures (i.e. model structures for the categories of $$n$$-polynomial and $$n$$-homogeneous functors) and realise the constructions of M. Weiss [Trans. Am. Math. Soc. 347, No. 10, 3743–3796 (1995); erratum ibid. 359, No. 2, 851–855 (1998; Zbl 0866.55020)] as Quillen functors on model categories. As an application of this new general interesting perspective they establish a stable variant of orthogonal calculus, replacing pointed topological spaces with orthogonal spectra.

##### MSC:
 55P42 Stable homotopy theory, spectra 55P91 Equivariant homotopy theory in algebraic topology 55U35 Abstract and axiomatic homotopy theory in algebraic topology
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##### References:
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