  We introduce the notion of categorical absorption of singularities: an
operation that removes from the derived category of a singular variety a small
admissible subcategory responsible for singularity and leaves a smooth and
proper category. We construct (under appropriate assumptions) a categorical
absorption for a projective variety $X$ with isolated ordinary double points.
We further show that for any smoothing $\mathcal{X}/B$ of $X$ over a smooth
curve $B$, the smooth part of the derived category of $X$ extends to a smooth
and proper over $B$ family of triangulated subcategories in the fibers of
$\mathcal{X}$.
