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...