Section IdentityMorphism.
Variable gT : finGroupType.
Implicit Types A B : {set gT}.
Implicit Type G : {group gT}.
Definition idm of {set gT} := fun x : gT => x : FinGroup.sort gT.
Canonical comp_morphism := Morphism comp_morphM.
Canonical factm_morphism := Morphism factm_morphM.

Lemma ker_factm_loc (K : {group aT}) : 'ker_(q @* K) ff = q @* 'ker_K f.