Canonical swapXY_rmorphism := AddRMorphism swapXY_is_multiplicative.Canonical swapXY_linear := AddLinear swapXY_is_scalable.

Lemma swapXY_map (R S : ringType) (f : {additive R -> S}) u : swapXY (u ^ map_poly f) = swapXY u ^ map_poly f.