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(*                                                                    *)
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(*                                                                    *)
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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	                CoUniversal Arrows               		     *)
(*									     *)
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(*									     *)
(*                            A.SAIBI   May 95				     *)
(*									     *)
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Require Export UniversalArrow.
Require Export Dual_Functor.
Set Implicit Arguments.
Unset Strict Implicit.
(* coUA *)
Section coua_def.
Variables (A B : Category) (b : B) (F : Functor A B).
Section iscoua_def.
Variables (a : A) (u : F a --> b).
Section coua_laws.
Variable co_diese : forall a' : A, (F a' --> b) -> (a' --> a).
Definition CoUA_eq (a' : A) (f : F a' --> b) (g : a' --> a) :=
FMor F g o u =_S f.
Definition CoUA_law1 :=
forall (a' : A) (f : F a' --> b), CoUA_eq f (co_diese f).
Definition CoUA_law2 :=
forall (a' : A) (f : F a' --> b) (g : a' --> a),
CoUA_eq f g -> g =_S co_diese f.
End coua_laws.
Structure IsCoUA : Type :=
{CoUA_diese : forall a' : A, (F a' --> b) -> (a' --> a);
Prf_isCoUA_law1 : CoUA_law1 CoUA_diese;
Prf_isCoUA_law2 : CoUA_law2 CoUA_diese}.
Variable t : IsCoUA.
(* f=g => f# = g# *)

Lemma Codiese_map : forall a' : A, Map_law (CoUA_diese t (a':=a')).
End iscoua_def.