In a Tikz commutative diagram, I would like to draw two parallel arrows that cross over. Something like this:
A x B | | | | \ / X f / \ | | V V C x D
(of course I would prefer the arrows to bend smoothly rather than have sharp corners).
(Here f is a map from the product A x B to the product C x D, and I want to visually suggest the fact this if f sends say a pair (a, b) to a pair (c, d), then c depends only on b and not on a, and d depends only on a and not on b.)
Does anyone know a simple way to do this? If it is impossible in Tikz-CD, maybe it is possible with another package?
Bonus points if it is possible to adjust the separation between the two arrows.