it is known that the duals of feedback-set problems are set-packing problems; in the context of digraphs the feedback set are either a minimal set of vertices or edges that hit every oriented cycle; the dual is then a cycle-packing of minimal weight (if I understood right)

Question:how are the graphs that represent the respective dual problems defined, e.g. how can the graph $H$ that represents the cycle-packing problem dual of the minimum feedback-vertex set problem that is represented by graph $G$ (and vice versa)?