In his study of quantum groups, Drinfeld suggested considering set-theoretic solutions of the Yang–Baxter equation as a discrete analogon. As a typical example, every conjugacy class in a group or, more generally, every rack
Q
Q
provides such a Yang–Baxter operator
c
Q
:
x
⊗
y
↦
y
⊗
x
y
c_Q \colon x \otimes y \mapsto y \otimes x^y
. In this article we study deformations of
c
Q
c_Q
within the space of Yang–Baxter operators over some complete ring. Infinitesimally these deformations are classified by Yang–Baxter cohomology. We show that the Yang–Baxter cochain complex of
c
Q
c_Q
homotopy-retracts to a much smaller subcomplex, called quasi-diagonal. This greatly simplifies the deformation theory of
c
Q
c_Q
, including the modular case which had previously been left in suspense, by establishing that every deformation of
c
Q
c_Q
is gauge equivalent to a quasi-diagonal one. In a quasi-diagonal deformation only behaviourally equivalent elements of
Q
Q
interact; if all elements of
Q
Q
are behaviourally distinct, then the Yang–Baxter cohomology of
c
Q
c_Q
collapses to its diagonal part, which we identify with rack cohomology. This establishes a strong relationship between the classical deformation theory following Gerstenhaber and the more recent cohomology theory of racks, both of which have numerous applications in knot theory.