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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*	            Existence of Left Adjoint                		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Adj_UA.
Set Implicit Arguments.
Unset Strict Implicit.
(* Maintenant a` partir d'un UA unit (pour tout d:D), *)
(* construire une adj *)
Section ua_to_ladj.
Variables (C D : Category) (G : Functor C D).
Hypothesis UA_of : forall d : D, UA d G.
Definition AdjointUA_ob (d : D) := UA_ob (UA_of d).
Section adjoint_ua_map_def.
Variable d d' : D.
Definition AdjointUA_mor (f : d --> d') :=
UA_diese (UA_of d) (f o UA_mor (UA_of d')).

(* Specifications: *)
Lemma AdjointUA_map_law : Map_law AdjointUA_mor.
Canonical Structure AdjointUA_map :
Map (d --> d') (AdjointUA_ob d --> AdjointUA_ob d') := AdjointUA_map_law.