Link invariants from finite categorical groups (Q5963050)

The paper develops a new invariant of tangles and framed tangles, defined over a finite crossed module and a pair of functions, called a Reidemeister pair, satisfying certain properties. Several concrete instances of the invariant are constructed from racks and quandles, and from central extensions of groups. It is shown that the new invariant includes all rack and quandle cohomology invariants, and it is stronger than the Eisermann invariant.