  We construct functors categorifying the branching rules for
$U_q(\mathfrak{g})$ for $\mathfrak{g}$ of type $B_n$, $C_n$, and $D_n$ for the
embeddings $so_{2n+1}\supset so_{2n-1}$, $sp_{2n}\supset sp_{2n-2}$, and
$so_{2n}\supset so_{2n-2}$. We give the corresponding categorical
Gelfand-Tsetlin basis.
