  Yang-Baxter (YB) deformations of type IIB string theory have been well
studied from the viewpoint of classical integrability. Most of the works,
however, are focused upon the local structure of the deformed geometries and
the global structure still remains unclear. In this work, we reveal a
non-geometric aspect of YB-deformed backgrounds as $T$-fold by explicitly
showing the associated $\mathrm{O}(D,D;\mathbb{Z})$ $T$-duality monodromy. In
particular, the appearance of an extra vector field in the generalized
supergravity equations (GSE) leads to the non-geometric $Q$-flux. In addition,
we study a particular solution of GSE that is obtained by a non-Abelian
$T$-duality but cannot be expressed as a homogeneous YB deformation, and show
that it can also be regarded as a $T$-fold. This result indicates that
solutions of GSE should be non-geometric quite in general beyond the YB
deformation.
