Edge-coloured graph homomorphisms, paths, and duality

We present a edge-coloured analogue of the duality theorem for transitive tournaments and directed paths. Given a edge-coloured path $P$ whose edges alternate blue and red, we construct a edge-coloured graph $D$ so that for any edge-coloured graph $G$ $$P\to G\iff G\to ̸D\mathrm{.}$$ The duals are simple to construct, in particular $\mathrm{\mid }V(D)\mathrm{\mid }=\mathrm{\mid }V(P)\mathrm{\mid }-1$.