Chris, Anindya and John:

Thanks for clearing up the Category vs. Category of Category mix up. You can always count on me falling into every trap/hole possible along the way. LOL.

So I basically now realized the huge difference between \\(\mathcal{C} \to \mathbf{Set}\\) and \\(\mathbf{Cat} \to \mathbf{Set}\\).

This would also mean that the category of \\(\mathbf{Preord}\\) doesn't necessarily have to have at most one morphism like a preorder but all of that information is trapped inside the object? These bold-faced categories are categories of a higher level in that the structure of the category doesn't actually reflect the actual structure of the object? For some odd reason, I was thinking this way which probably caused the level slip...

Thanks for clearing up the Category vs. Category of Category mix up. You can always count on me falling into every trap/hole possible along the way. LOL.

So I basically now realized the huge difference between \\(\mathcal{C} \to \mathbf{Set}\\) and \\(\mathbf{Cat} \to \mathbf{Set}\\).

This would also mean that the category of \\(\mathbf{Preord}\\) doesn't necessarily have to have at most one morphism like a preorder but all of that information is trapped inside the object? These bold-faced categories are categories of a higher level in that the structure of the category doesn't actually reflect the actual structure of the object? For some odd reason, I was thinking this way which probably caused the level slip...