An Operator on bordered Khovanov homology induced by 2-cabling.

We use Bar-Natan's planar algebra formalism to construct an operator on type D structures over the Bar-Natan algebra induced by 2-cabling. This operator is concrete and computable, and the resulting functor on the Fukaya category of the 4-punctured sphere is somewhat interesting, in that its behaviour differs from a similar functor constructed by Hanselman and Watson.