ScalingStacks

Proposition 31 Let $D$ be a diagram with $n$ crossings and $D^{!}$ the dual diagram (see above). Then the commutative $\mathcal{I}$-cube ${\cal V}_{D^{!}}\{-n\}$ is isomorphic to the dual $({\cal V}_{D})^{\ast}$ of the $\mathcal{I}$-cube ${\cal V}_{D}.$