Local Framings

TL;DR

This paper explores the structure of stable frames and their compatibility with Bousfield localisation to deepen understanding of the stable homotopy category and algebraic model categories.

Contribution

It introduces a structured approach to stable frames, examining their interaction with Bousfield localisation and applications to rigidity and algebraic model categories.

Findings

Stable frames can be constructed from spectra to stable model categories.

Compatibility of stable frames with Bousfield localisation provides new insights.

Techniques relate to rigidity questions and algebraic model categories.

Abstract

Framings provide a way to construct Quillen functors from simplicial sets to any given model category. A more structured set-up studies stable frames giving Quillen functors from spectra to stable model categories. We will investigate how this is compatible with Bousfield localisation to gain insight into the deeper structure of the stable homotopy category. We further show how these techniques relate to rigidity questions and how they can be used to study algebraic model categories.