A Dwyer-Rezk classification for polynomial functors in Weiss calculus
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915638646145024 |
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| author | Barnes, David Kędziorek, Magdalena Taggart, Niall |
| author_facet | Barnes, David Kędziorek, Magdalena Taggart, Niall |
| contents | In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving $d$-excisive functors from pointed spaces to spectra as spectrum-valued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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Dwyer-Rezk classification for polynomial functors in Weiss calculus Barnes, David Kędziorek, Magdalena Taggart, Niall Algebraic Topology 18F50, 55P65, 55P42 In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving $d$-excisive functors from pointed spaces to spectra as spectrum-valued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. |
| title | A Dwyer-Rezk classification for polynomial functors in Weiss calculus |
| topic | Algebraic Topology 18F50, 55P65, 55P42 |
| url | https://arxiv.org/abs/2508.03808 |