End FunctorGroup.
Canonical gFmod_group
(F1 : GFunctor.iso_map) (F2 : GFunctor.object_map)
(gT : finGroupType) (G : {group gT}) :=
[group of (F1 %% F2)%gF gT G].
Section IsoFunctorTheory.
Implicit Types gT rT : finGroupType.
Variable F : GFunctor.iso_map.

(* Specifications: *)
Lemma gFsub gT (G : {group gT}) : F gT G \subset G.
Lemma gFnorm gT (G : {group gT}) : G \subset 'N(F gT G).
Lemma injmF gT rT (G D : {group gT}) (f : {morphism D >-> rT}) :
'injm f -> G \subset D -> f @* (F gT G) = F rT (f @* G).
Lemma gFisom gT rT (G D : {group gT}) R (f : {morphism D >-> rT}) :
G \subset D -> isom G (gval R) f -> isom (F gT G) (F rT R) f.
Lemma gFisog gT rT (G : {group gT}) (R : {group rT}) :
G \isog R -> F gT G \isog F rT R.