 For example, every graph is a coalgebra of  ℘  on  F :  Set → Set. That is, every graph  (G,→)  may be re-packaged  as  (G, e), with e : G →  ℘   G  given by  e(x) = {y ∈ G :        x→ y}.   In words, we trade in the  edge relation of a graph with the function that assigns to each point its set of children.    This re-packaging has an inverse, and so the notions of “graph as set with relation” and “graph as coalgebra of ℘”  are in this sense notational variants.[12]