Localisation of cubical model categories
Brice Le Grignou
TL;DR
This paper introduces square structures on model categories, generalizing cubical model categories, and demonstrates that under certain conditions, the resulting cubical category is a localization of the original model category.
Contribution
It proposes a new notion of square structure on model categories, extending cubical model categories, and establishes conditions for their localization.
Findings
Square structures generalize cubical model categories
Under homotopical conditions, the cubical category is a localization
Provides a framework for cubical localization in model categories
Abstract
In this article we introduce the notion of a square structure on a model category, that generalises cubical model categories. We then show that under some homotopical conditions on this square structure the induced cubical category is a localisation of the model category.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra