A Dwyer-Rezk classification for polynomial functors in Weiss calculus

Abstract

In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving $d$-excisive functors from pointed spaces to spectra as spectrum-valued functors on the category of finite sets of cardinality at most $d$ and epimorphisms. We prove through different methods the analogous result in Weiss calculus: $d$-polynomial functors are equivalent to spectrum-valued functors on the category of finite-dimensional inner product spaces of dimension at most $d$ and orthogonal epimorphisms. Via similar methods we obtain a new proof of the classification of homogeneous functors.