Matthew wrote :

>The short answer: is because partial orders are \\(\mathbf{Bool}\\)-categories, and a monotone function is exactly the same as a functor between \\(\mathbf{Bool}\\)-categories .

Doh. We learned this... sorry forgot that preorders are just \\(\mathbf{Bool}\\)-categories. I think I've been learning too much in short period of time LOL. Thanks for the kind answer.

>The short answer: is because partial orders are \\(\mathbf{Bool}\\)-categories, and a monotone function is exactly the same as a functor between \\(\mathbf{Bool}\\)-categories .

Doh. We learned this... sorry forgot that preorders are just \\(\mathbf{Bool}\\)-categories. I think I've been learning too much in short period of time LOL. Thanks for the kind answer.