Categories of skew left braces and trifactorised groups

TL;DR

This paper explores the deep connections between skew left braces and trifactorised groups, focusing on their structures, quotients, and homomorphisms to enhance understanding of their algebraic properties.

Contribution

It introduces a detailed framework linking skew left braces with trifactorised groups, revealing new structural insights and relationships.

Findings

Established a correspondence between skew left braces and trifactorised groups

Characterized quotients and homomorphisms within this framework

Provided new structural classifications for skew left braces

Abstract

The main objective of this paper is to deepen the relationship between skew left braces and trifactorised groups that encodes the information about skew left braces, their structure, their quotients, and their homomorphisms.