Categories of Skew Left Braces and Trifactorised Groups

Key Points

• The aim is to explore the connections between skew left braces and trifactorised groups to enhance understanding of their structures and properties.
• Analyzed the definitions and properties of skew left braces and trifactorised groups.
• Investigated their structural characteristics and quotient formations.
• Examined homomorphisms related to these mathematical constructs.
• Established significant links between the structure of skew left braces and trifactorised groups.
• Identified new perspectives on the quotients of skew left braces.
• Showed how homomorphisms contribute to understanding these algebraic structures.