Work

A Dwyer–Rezk classification for polynomial functors in Weiss calculus

Year: 2026

Type: article

Abstract: In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving d d -excisive functors from pointed spaces to spectra as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

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/17584

Authors: David Barnes, Magdalena Kędziorek, Niall Taggart

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Isaac Newton Institute for Mathematical Sciences, Fondation des Treilles, Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: Isaac Newton Institute for Mathematical Sciences (INI), G2295911252, G2865665362, G3449727034, The periodic homotopy type of spaces of embeddings, G4550126978, G49378810, G5248526158, G5415612579, G5826069933, Commutativity in the world of symmetry, G7480577876

OpenAlex ID: W4416788686

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