Here is my attempt at **Puzzle 66**.

The condition of the monoidal preorder arises if \\(\otimes\\) is a _monotone_ map between the product preorder \\(X \times X\\) and the original preorder \\(X\\).

If \\(\otimes\\) is a monotone map then, for all pairs \\( (x, y), (x' , y') \in X \times X \\), we have:

- \\((x, y) \le_{X \times X} (x', y')\\) implies \\(x \otimes y \le_{X} x' \otimes y'\\).

Using the definition of the relation \\(\le_{X \times X}\\) in the product preorder, we arrive at the condition of the monoidal preorder:

- \\(x \le_X x'\\) and \\(y \le_X y'\\) imply \\(x \otimes y \le_{X} x' \otimes y'\\).