  We define an invariant of tangles and framed tangles given a finite crossed
module and a pair of functions, called a Reidemeister pair, satisfying natural
properties. We give several examples of Reidemeister pairs derived from racks,
quandles, rack and quandle cocycles, and central extensions of groups. We prove
that our construction includes all rack and quandle cohomology (framed) link
invariants, as well as the Eisermann invariant of knots. We construct a class
of Reidemeister pairs which constitute a lifting of the Eisermann invariant,
and show through an example that this class is strictly stronger than the
Eisermann invariant itself.
