Internal categories in 2-category of 2-groups

The aim of this talk is to discuss the 2-dimensional analogue of the well-known equivalence between crossed modules and internal categories in the category of groups. I will point out the role of 2-categorical limits both in defining categories internally to a 2-category and in constructing the equivalence between internal categories in the 2-category of 2-groups and 2-crossed modules. I will also briefly discuss the notions of normal sub-2-group and central extension induced by the notion of 2-crossed module.

Enrico Vitale-s homepage