In Barry Simon's Representations of finite and compact groups he refers to the set of irreps (or rather equivalence classes thereof) of a given finite group $G$ as the “dual object” $\widehat G$
Definition $\widehat G$, the dual object, is the set of equivalence classes of irreps, each class consisting of unitarily equivalent irreps. (p. 25)
I can't seem to find this terminology being used anywhere else, but in what sense is this duality meant? What structure warranting invocation of “duality” does the dual object have besides its cardinality equalling the number of conjugacy classes?