1) Any \\(\alpha_c\\) in \\( \mathcal{P} \\) is unique, because \\( \mathcal{P} \\) is a preorder meaning at most 1 arrow exists between a pair of objects.

![One Natural Transformation](https://docs.google.com/drawings/d/e/2PACX-1vSrQVA_5UJFCXyLjDq4aNZehvlM4rWuM7o8UxKPAzl4YihE1daYEkvbws_5G9089Dej9B4N5Z7JcoMB/pub?w=607&h=383)

2) There is nothing in \\( \mathcal{C} \\) restricting the number of arrows between a pair of objects.

![Two Natural Transformations](https://docs.google.com/drawings/d/e/2PACX-1vR_x8gK_X_cK3UcOTO8PAiMeu2bILBjwg8Fq6fz5g9PaWxkr2XY55VRM1pkAtEsd-k2XWXTmOZOvfrw/pub?w=786&h=406)