  Given a rack Q and a ring A, one can construct a Yang-Baxter operator c_Q: V
tensor V --> V tensor V on the free A-module V = AQ by setting c_Q(x tensor y)
= y tensor x^y for all x,y in Q. In answer to a question initiated by D.N.
Yetter and P.J. Freyd, this article classifies formal deformations of c_Q in
the space of Yang-Baxter operators. For the trivial rack, where x^y = x for all
x,y, one has, of course, the classical setting of r-matrices and quantum
groups. In the general case we introduce and calculate the cohomology theory
that classifies infinitesimal deformations of c_Q. In many cases this allows us
to conclude that c_Q is rigid. In the remaining cases, where infinitesimal
deformations are possible, we show that higher-order obstructions are the same
as in the quantum case.
