  Codimension two defects of the $(0,2)$ six dimensional theory
$\mathscr{X}[\mathfrak{j}]$ have played an important role in the understanding
of dualities for certain $\mathcal{N}=2$ SCFTs in four dimensions. These
defects are typically understood by their behaviour under various dimensional
reduction schemes. In their various guises, the defects admit partial
descriptions in terms of singularities of Hitchin systems, Nahm boundary
conditions or Toda operators. Here, a uniform dictionary between these
descriptions is given for a large class of such defects in
$\mathscr{X}[\mathfrak{j}], \mathfrak{j} \in A,D,E$.
