  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, 2-crossed modules and braided crossed
modules. We prove that our construction includes all rack and quandle
cohomology (framed) link invariants, as well as the Eisermann invariant of
knots, for which we also find a lifting by using braided crossed modules.
