In this study, we investigate the relationships between the category of crossed modules of groups and the category of whiskered groupoids. Our first aim is to construct a crossed module structure over groups from a whiskered groupoid with the objects set - a group (regular groupoid) - using the usual functor between the categories of crossed modules and cat groups. Conversely, the second aim is to construct a whiskered groupoid structure with the objects set, which is a group, from a crossed module of groups. While establishing this relationship, we frequently used arrow diagrams representing morphisms to make the axioms more comprehensible. We provide the conditions for the bimorphisms in a whiskered groupoid and give the relations between this structure and internal groupoids in the category of whiskered groupoids with the objects set as a group.
Birincil Dil | İngilizce |
---|---|
Konular | Cebir ve Sayı Teorisi, Kategori Teorisi, K Teorisi, Homolojik Cebir, Topoloji |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Erken Görünüm Tarihi | 28 Mart 2024 |
Yayımlanma Tarihi | 29 Mart 2024 |
Gönderilme Tarihi | 12 Aralık 2023 |
Kabul Tarihi | 22 Şubat 2024 |
Yayımlandığı Sayı | Yıl 2024 Sayı: 46 |
As of 2021, JNT is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC). |