2025/07/23 by Niall Taggart, Taggart, Niall
Computer Science · #18F50 #18N55 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.2507.17321
openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.