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.
Definition morphm of morphic f := f : aT -> FinGroup.sort rT.
Canonical morphm_morphism fM := @Morphism _ _ A (morphm fM) (morphicP fM).
End MorphicProps.

Lemma misomP f : reflect {fM : morphic f & isom (morphm fM)} (misom f).