End Homg.
Arguments homg _ _ _%g _%g.
Notation "G \homg H" := (homg G H)
(at level 70, no associativity) : group_scope.
Arguments homgP {rT aT C D}.
(* Isomorphism between a group and its subtype. *)
Section SubMorphism.
Variables (gT : finGroupType) (G : {group gT}).
Canonical sgval_morphism := Morphism (@sgvalM _ G).
Canonical subg_morphism := Morphism (@subgM _ G).

(* Specifications: *)
Lemma injm_sgval : 'injm sgval.
Lemma sgval_sub A : sgval @* A \subset G.
Lemma subgmK (A : {set gT}) : A \subset G -> sgval @* (subg G @* A) = A.
Lemma im_sgval : sgval @* [subg G] = G.