Homological Localisation of Model Categories
David Barnes, Constanze Roitzheim
TL;DR
This paper introduces a new method for localising stable model categories at a spectrum E, extending the tools for studying the stable homotopy category and connecting to known categories.
Contribution
It proposes a candidate for E-localisation in arbitrary stable model categories and analyzes its properties and relationships to established categories.
Findings
The new localisation construction behaves well with respect to known properties.
It relates the E-localisation to well-understood categories in stable homotopy theory.
The approach provides a framework for further exploration of localisations in model categories.
Abstract
One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E-localisation of this model category. We study the properties of this new construction and relate it to some well-known categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra