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.
Primary Language | English |
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Subjects | Algebra and Number Theory, Category Theory, K Theory, Homological Algebra, Topology |
Journal Section | Research Article |
Authors | |
Early Pub Date | March 28, 2024 |
Publication Date | March 29, 2024 |
Submission Date | December 12, 2023 |
Acceptance Date | February 22, 2024 |
Published in Issue | Year 2024 Issue: 46 |
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