Representation of actions of 3-groups: Actor crossed square and actor cat2-group

Çağlayan E. I.

Journal of Algebra and its Applications, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s0219498826502993
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: action, actor, cat2-group, Crossed square, split extension classifier
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

Actor in categories of interest was given in [J. M. Casas, T. Datuashvilli and M. Ladra, Universal strict general actors and actors in categories of interest, Appl. Categ. Struct. 18 (2010) 85–114]. It is well known that the category of crossed squares of groups, Crs2(Grp), and the category of cat2-group, Cat2(Grp), are equivalent from [J. L. Loday, Spaces with finitely many nontrivial homotopy groups, J. Pure Appl. Algebra 24 (1982) 179–202]. Also,we know that the category Cat2(Grp) is a category of interest. By using these properties, we construct an actor of a cat2-group and that of crossed square of groups. Hence, we also obtain the split extension classifier of the corresponding crossed square, which give rise to the representability of actions in the category of crossed squares.