# On Regular Representation of 2-Crossed Modules and Cat2-Groups

## 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.

## Key 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.

---
Source: https://tomesphere.com/paper/2302.12641