In some sense, in the pictures it would be more sensible to put \\(Y\\) *on top of* \\(X\\). One can think (sometimes usefully, sometimes less usefully) of a feasability relation (or profunctor) between preorders as giving rise to a new preorder, known as the **collage**. The underlying set of the collage is the disjoint union \\(X \sqcup Y\\) and on both \\(X\\) and \\(Y\\) the new preorder restricts to the preorders you started with, but for all \\(x \in X\\) and \\(y \in Y\\) you have \\(y\not\le x\\) whilst \\(x\le y\, \iff\ \Phi(x,y)\\).

The pictures drawn with the blue arrows are the Hasse diagrams of these collages. Nothing in \\(Y\\) ever comes before anything in \\(X\\) in this preorder, so that's why it would make sense to draw \\(Y\\) on top of \\(X\\). I'll leave it for someone to produce such a version of the examples above :-).

The pictures drawn with the blue arrows are the Hasse diagrams of these collages. Nothing in \\(Y\\) ever comes before anything in \\(X\\) in this preorder, so that's why it would make sense to draw \\(Y\\) on top of \\(X\\). I'll leave it for someone to produce such a version of the examples above :-).