In this paper we introduce and study the categorical group of derivations from a categorical group into a braided categorical group equipped with a given coherent left action of . Categorical groups provide a 2-dimensional vision of groups and so this object is a sort of 0-cohomology at a higher...

For any categorical group ℍ, we introduce the categorical group (ℍ) and then the well-known group exact sequence 1 → () → → () → () → 1 is raised to a categorical group level by using a suitable notion of exactness. Breen's Schreier theory for extensions of categorical groups is...