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(*                                                                    *)
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(*                                                                    *)
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(* 02110-1301 USA                                                     *)


(*****************************************************************************)
(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
(*****************************************************************************)
(*									     *)
(*	                     Identity Functor             		     *)
(*									     *)
(*****************************************************************************)
(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
(*****************************************************************************)


Require Export Functor.

Set Implicit Arguments.
Unset Strict Implicit.

(* Id(C) : C -> C *)

Section idCat.

Variable C : Category.

Definition Id_CAT_ob (a : C) := a.
                      
Definition Id_CAT_map (a b : C) := Id_map (a --> b).
                   
Lemma Id_CAT_comp_law : Fcomp_law (FOb:=Id_CAT_ob) Id_CAT_map.
Proof.
(* Goal: @Fcomp_law C C Id_CAT_ob Id_CAT_map *)
unfold Fcomp_law in |- *; intros; apply Refl.
Qed.

Lemma Id_CAT_id_law : Fid_law (FOb:=Id_CAT_ob) Id_CAT_map.
Proof.
(* Goal: @Fid_law C C Id_CAT_ob Id_CAT_map *)
unfold Fid_law, Id_CAT_ob in |- *; intros a; apply Refl.
Qed.

Canonical Structure Id_CAT := Build_Functor Id_CAT_comp_law Id_CAT_id_law.

End idCat.



