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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 Right Adjoint                		     *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Adj_UA.
Set Implicit Arguments.
Unset Strict Implicit.
Section ua_to_radj.
Variables (C D : Category) (F : Functor D C).
Hypothesis UA_of : forall c : C, CoUA c F.
(* construction de l'adj droit *)
Definition CoadjointUA_ob (c : C) := CoUA_ob (UA_of c).
Section coadjoint_ua_map_def.
Variable c c' : C.
Definition CoadjointUA_mor (f : c --> c') :=
CoUA_diese (UA_of c') (CoUA_mor (UA_of c) o f).

Lemma CoadjointUA_map_law : Map_law CoadjointUA_mor.
Canonical Structure CoadjointUA_map :
Map (c --> c') (CoadjointUA_ob c --> CoadjointUA_ob c') :=
CoadjointUA_map_law.