Whiskered Groupoids and Crossed Modules with Diagrams

Authors : Zeynep Güler, Erdal Ulualan

Pages : 23-39

Doi:10.53570/jnt.1403803

View : 65 | Download : 62

Publication Date : 2024-03-29

Article Type : Research

Abstract :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.
Keywords : Groupoid, crossed module, whiskered categories, bimorphism