arXiv Open Access 2022

Coverings and liftings of generalized crossed modules

Gamze Aytekin Arici Tunçar Şahan

Lihat Sumber

Abstrak

In the theory of crossed modules, considering arbitrary self-actions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of generalized crossed module emerges. In this paper we give a precise definition for generalized cat$^1$-groups and obtain a functor from the category of generalized cat$^1$-groups to generalized crossed modules. Further, we introduce the notions of coverings and liftings for generalized crossed modules and investigate properties of these structures. Main objective of this study is to obtain an equivalence between the category of coverings and the category of liftings of a given generalized crossed module $(A,B,α)$.

Topik & Kata Kunci

math.CT math.GR

Penulis (2)

Gamze Aytekin Arici

Tunçar Şahan

Format Sitasi

APA MLA BibTeX

Arici, G.A., Şahan, T. (2022). Coverings and liftings of generalized crossed modules. https://arxiv.org/abs/2204.05661

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2022
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓