Now that I think about it, the answer in puzzle 170 implies the answer in puzzle 169.

But to answer 170, a morphism \$$h\$$ in \$$\mathcal{C} \times \mathcal{D}\$$ is equal to a pair of morphisms, one morphism \$$f\$$ in \$$\mathcal{C}\$$ and a morphism \$$g\$$ in \$$\mathcal{D}\$$,

\$h: \mathcal{C} \times \mathcal{D} \to \mathcal{C} \times \mathcal{D} \\\\ h = \langle f, g \rangle \$

Setting, \$$\mathcal{C}\$$ to \$$X^{op}\$$, \$$\mathcal{D}\$$ to \$$Y\$$, \$$f\$$ to \$$\leq\_{X^{op}}\$$ and \$$g\$$ to \$$\leq_Y\$$ answers question 169.