On tested Bousfield-Friedlander localizations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908462212972544 |
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| author | Taggart, Niall |
| author_facet | Taggart, Niall |
| contents | We demonstrate that a Bousfield-Friedlander localization with a set of test morphisms in the sense introduced by Bandklayder, Bergner, Griffiths, Johnson, and Santhanam can also be characterized as a left Bousfield localization at the set of test morphisms. This viewpoint enables us to establish a homogeneous model structure associated with any calculus arising from a Bousfield-Friedlander localization of this form. As a corollary, we show that homogeneous functors in discrete calculus coincide up to homotopy with those in Goodwillie calculus. Finally, we illustrate this framework by proving that the polynomial model structure of Weiss calculus is a particular instance of tested Bousfield-Friedlander localization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On tested Bousfield-Friedlander localizations Taggart, Niall Algebraic Topology Category Theory 18N55, 18F50 We demonstrate that a Bousfield-Friedlander localization with a set of test morphisms in the sense introduced by Bandklayder, Bergner, Griffiths, Johnson, and Santhanam can also be characterized as a left Bousfield localization at the set of test morphisms. This viewpoint enables us to establish a homogeneous model structure associated with any calculus arising from a Bousfield-Friedlander localization of this form. As a corollary, we show that homogeneous functors in discrete calculus coincide up to homotopy with those in Goodwillie calculus. Finally, we illustrate this framework by proving that the polynomial model structure of Weiss calculus is a particular instance of tested Bousfield-Friedlander localization. |
| title | On tested Bousfield-Friedlander localizations |
| topic | Algebraic Topology Category Theory 18N55, 18F50 |
| url | https://arxiv.org/abs/2507.17321 |