Section Homg.
Implicit Types rT gT aT : finGroupType.
Definition homg rT aT (C : {set rT}) (D : {set aT}) :=
[exists (f : {ffun aT -> rT} | morphic D f), f @: D == C].

Lemma eq_homgr gT rT aT (G : {group gT}) (H : {group rT}) (K : {group aT}) :
G \isog H -> homg K G = homg K H.