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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	            Adjunction Example : CCC                		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Cartesian1.
Require Export CCC.
Require Export FunProd.
Set Implicit Arguments.
Unset Strict Implicit.
(* construire l'expo... a` partir d'un CCC *)
Section funprod_hasexpo.
Variable C : Category.
Variable H : HasBinProd C.
Definition HasExponent1 := forall a : C, RightAdj (Fun_prod H a).
Variable H1 : HasExponent1.
Section funprod_expo.
Variable a b : C.
Let ua' := CoUnit (H1 a) b.
Definition Expo1 := CoUA_ob ua'.
Definition Eval1 := CoUA_mor ua'.
Section lambda1_def.
Variable c : C.
Definition Lambda1_mor (f : H_obj_prod H c a --> b) := CoUA_diese ua' f.

(* Specifications: *)
Lemma Lambda1_map_law : Map_law Lambda1_mor.
Canonical Structure Lambda1 := Build_Map Lambda1_map_law.