A higher-dimensional categorical perspective on 2-crossed modules
DEMONSTRATIO MATHEMATICA, cilt.57, sa.1, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 57 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.1515/dema-2024-0061
- Dergi Adı: DEMONSTRATIO MATHEMATICA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
- Eskişehir Osmangazi Üniversitesi Adresli: Evet
Özet
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.