On Regular Representation of 2-Crossed Modules and Cat2-Groups
Murat Sarikaya, Erdal Ulualan
TL;DR
This paper explores the regular representation of 2-crossed modules and their related Gray 3-group groupoids, extending classical concepts to higher categorical structures and providing a Cayley-type theorem.
Contribution
It introduces a regular representation framework for 2-crossed modules and associated Gray 3-group groupoids, linking them via Cayley theorem analogs.
Findings
Establishment of a Cayley theorem for 2-crossed modules
Description of regular representations for Gray 3-group groupoids
Connection between 2-crossed modules and cat2-groups
Abstract
In this paper, we describe a regular representation given by Cayley theorem for 2-crossed modules of groups and their associated Gray 3-group groupoids with a single 0-cell and equivalently cat2-groups.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology