  We introduce the notion of a simultaneous categorical resolution of
singularities, a categorical version of simultaneous resolutions of rational
double points of surface degenerations. Furthermore, we suggest a construction
of simultaneous categorical resolutions which, in particular, applies to the
case of a flat projective 1-dimensional family of varieties of arbitrarily high
even dimension with ordinary double points in the total space and central
fiber. As an ingredient of independent interest, we check that the property of
a geometric triangulated category linear over a base to be relatively smooth
and proper can be verified fiberwise. As an application we construct a smooth
and proper family of K3 categories with general fiber the K3 category of a
smooth cubic fourfold and special fiber the derived category of the K3 surface
of degree 6 associated with a singular cubic fourfold.
