Cubical model categories and quasi-categories
Brice Le Grignou
TL;DR
This paper explores the use of cubical sets in enriched categories and infinity-categories, demonstrating their effectiveness in describing complex structures in homological algebra.
Contribution
It highlights the role of cubical sets in modeling infinity-categories and their application in homological algebra, offering a new perspective in higher category theory.
Findings
Cubical sets effectively model infinity-categories.
Enriched categories in cubical sets facilitate descriptions in homological algebra.
The approach provides a convenient framework for complex categorical structures.
Abstract
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many infinity-categories appearing in the context of homological algebra.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra