1) How is $\triangle A$ defined on a morphism $ f^{op}: V\to U$? $\triangle A(f^{op})$ should be a map of sets $A\to A$. Is there only one definition that will force functoriality?
2) How should I try to solve the problem itself? I.e., what strategy should I use? There must be a lot of functors $[\mathscr O(X)^{op},\mathbf{Set}]\to\mathbf{Set}$, so potentially there are a lot of choices for $\Pi$ (and similarly for the other functors).