  Every rack $Q$ provides a set-theoretic solution $c_Q$ of the Yang-Baxter
equation. This article examines the deformation theory of $c_Q$ within the
space of Yang-Baxter operators over a ring $\A$, a problem initiated by Freyd
and Yetter in 1989. As our main result we classify deformations in the modular
case, which had previously been left in suspense, and establish that every
deformation of $c_Q$ is gauge-equivalent to a quasi-diagonal one. Stated
informally, in a quasi-diagonal deformation only behaviourally equivalent
elements interact. In the extreme case, where all elements of $Q$ are
behaviourally distinct, Yang-Baxter cohomology thus collapses to its diagonal
part, which we identify with rack cohomology. The latter has been intensively
studied in recent years and, in the modular case, is known to produce
non-trivial and topologically interesting Yang-Baxter deformations.
