The double-optics doubling conjecture

Let $X,A,Y,B$ be objects of the underlying actegories, and let $((X,A),(Y,B))$ be an object of the category of double lenses over the optic category. A context on $((X,A),(Y,B))$ is equivalently a state

$$(I,I)\mathrel{\to}((X,A),(Y,B))$$

in the monoidal category of double lenses. Double-optics doubling conjecture. Categories of double optics are instances of the doubling, or CP, construction from categorical quantum mechanics. This conjecture proposes a categorical-quantum-mechanical explanation of the graphical structure of double optics; its resolution is not specified in the source.