Anindya wrote:

>for all \$$(x, y)\$$ and \$$(a, b)\$$. Unwrapping the left and right hand sides, this is equivalent to

>$\mathcal{X}(a, x) \otimes \mathcal{Y}(a, b) \leq \Phi(x, y) \multimap \Phi(a, b)$

>for all \$$a, x, y, b\$$. But the adjunction definition of \$$\multimap\$$ tells us that this is equivalent to

>$\Phi(x, y) \otimes \mathcal{X}(a, x) \otimes \mathcal{Y}(a, b) \leq \Phi(a, b)$

I think there is a typo. \$$\mathcal{Y}(a, b)\$$ should be \$$\mathcal{Y}(y, b)\$$?