Related to **Puzzle 11.**. Is it true that for a monotone map f:X->Y that has an inverse g:Y->X, there will always exist a monotone map h:Y->X [not necessarily g]?


I see from the example in https://forum.azimuthproject.org/discussion/comment/16151/#Comment_16151 . The problem is that the preorder Y may be equipped with arrows that are not representable in X.
Can you describe what type of arrows are problematic?