On tested Bousfield-Friedlander localizations

Fuente: arXiv
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Main Author: Taggart, Niall
Format: Preprint
Published: 2025
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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