1. A higher-dimensional categorical perspective on 2-crossed modules
- Author
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Özel Emre, Arslan Ummahan Ege, and İlker Akça İbrahim
- Subjects
crossed module ,2-crossed module ,categorification ,sestertius category ,tricategory ,18g45 ,18n10 ,18n20 ,18n25 ,Mathematics ,QA1-939 - Abstract
In this study, we will express the 2-crossed module of groups from a higher-dimensional categorical perspective. According to simplicial homotopy theory, a 2-crossed module is the Moore complex of a 2-truncated simplicial group. Therefore, the 2-crossed module is an algebraic homotopy model for the homotopy 3-types. Tricategories are a three-dimensional generalization of the bicategory concept. Any tricategory is triequivalent to the Gray category, where Gray is a category enriched over the monoidal category 2Cat equipped with the Gray tensor product. Briefly, a Gray category is a semi-strict 3-category for homotopy 3-types. Naturally, the tricategory perspective is used in homotopy theory. The 2-crossed module is associated with the concept of the Gray category. The aim of this study is to obtain a single object tricategory from any 2-crossed module of groups.
- Published
- 2024
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