Classification of abelian track categories (Q1611691)

A groupoid is said to be abelian if the automorphism group of each object is abelian. A track category is a 2-category where 2-cells form a groupoid. The paper shows that any abelian track category has canonically a structure of linear track extension. This structure was defined in order to describe the 3-cohomology of categories with abelian and functorial coefficients. A track category is then determined, up to weak equivalence, by a characteristic cohomology class: the universal Toda bracket.