End funct_setoid.
Infix "=_F" := Equal_Functor (at level 70).
(* composition of two functors *)
Section Comp_F.
Variables (C D E : Category) (G : Functor C D) (H : Functor D E).
Definition Comp_FOb (a : C) := H (G a).
Section comp_functor_map.
Variable a b : C.
Definition Comp_FMor (f : a --> b) := FMor H (FMor G f).

Lemma Comp_FMap_law : Map_law Comp_FMor.
Definition Comp_FMap :=
Build_Map (B:=Comp_FOb a --> Comp_FOb b) Comp_FMap_law.