Section comp_functor_map.
Variable a b : C.
Definition Comp_FMor (f : a --> b) := FMor H (FMor G f).
Definition Comp_FMap :=
Build_Map (B:=Comp_FOb a --> Comp_FOb b) Comp_FMap_law.
End comp_functor_map.

Lemma Comp_Functor_id_law : Fid_law Comp_FMap.