End Characteristicity.
Arguments characteristic _ _%g _%g.
Notation "H \char G" := (characteristic H G) : group_scope.
Hint Resolve char_refl : core.
Section InjmChar.
Variables (aT rT : finGroupType) (D : {group aT}) (f : {morphism D >-> rT}).
Hypothesis injf : 'injm f.

(* Specifications: *)
Lemma injm_char (G H : {group aT}) :
G \subset D -> H \char G -> f @* H \char f @* G.