@MatthewDoty wrote:

> In fact, the category of preorders is _bicartesian closed_. There's an initial preorder, a final preorder, products and coproducts and an exponential. If this is interesting we can go into this construction and the proof.

So:

* Initial preorder = empty set
* Final preorder = terminal preorder = singleton set

What are the exponential of two preorders? I'm guessing that \\(A^B\\) is the set of order preserving maps from \\(B\\) to \\(A\\), where the maps are ordered by pointwise comparisons: \\(f \le g\\) means \\(f(x) \le g(x)\\) for all \\(x\\).

Guessing again, is the coproduct formed by taking the disjoint union of the underlying sets, and the disjoint union of the ordering relations?