Rack and quandle

Summary

A rack is a set with a binary operation that distributes over itself and acts on the set by bijections. A quandle is a rack in which every element $a$ satisfies $a \triangleleft a = a$. The model example is conjugation in a group, $a \triangleleft b = a b a^{-1}$, which keeps the properties of conjugation and forgets the group multiplication. The three quandle axioms match the three Reidemeister moves of knot diagrams, so each knot has a fundamental quandle, which is a strong knot invariant.