Double groupoids and 2-groupoids in regular Mal'tsev categories

Key Points

• Double groupoids enhance the structure of regular mal'tsev categories by introducing additional morphisms—providing a more flexible algebraic framework.
• The study reveals that 2-groupoids can represent more complex relationships within categories, allowing for richer categorical behaviors.
• Analysis employs categorical structures to demonstrate the interaction between double groupoids and mal'tsev categories via functors and natural transformations.
• This groundwork could lead to new insights in homotopy theory and applications within algebraic topology or related fields.