Michael wrote in 37:
> The last two questions are still unclear to me...

Remember that in the case of a natural transformation \$$\alpha: F \rightarrow G \$$ you have two functors \$$F, G : \mathcal{C} \rightarrow \mathcal {D}\$$ and that for objects \$$A\$$ and \$$B\$$ in \$$\mathcal{C}\$$ and morphism \$$f : A \rightarrow B\$$ we need to have \$$\alpha_B \circ F(f) = G(f) \circ \alpha_A\$$

In this case we have functors \$$LP, RP: \mathcal{C} \times \mathcal{C} \times \mathcal{C} \rightarrow \mathcal{C} \$$ and we need to show that the following sqaures commute: