A Dwyer-Rezk classification for polynomial functors in Weiss calculus

2025/08/05 by Barnes, David, Kędziorek, Magdalena, Taggart, Niall
#18F50 #55P42 #55P65 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.03808

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In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving d-excisive functors from pointed spaces to spectra as spectrum-valued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.

Citations

• Polynomial functors from free groups to a stable infinity-category
• Homotopical recognition of diagram categories
• Koszul duality and a classification of stable Weiss towers
• The higher algebra of weighted colimits
• Symplectic Weiss calculi
• Noncommutative CW-spectra as enriched presheaves on matrix algebras
• Unitary calculus: model Categories and convergence
• Goodwillie calculus and Mackey functors
• Parametrized higher category theory and higher algebra: A general introduction
• A classification of Taylor towers of functors of spaces and spectra

Related

• Goodwillie calculus and Mackey functors
• Introduction to the manifold calculus of Goodwillie-Weiss
• A classification of Taylor towers of functors of spaces and spectra
• On spectra and affine strict polynomial functors
• The spectrum of excisive functors