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(* 02110-1301 USA                                                     *)
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(*          Projet Formel - Calculus of Inductive Constructions V5.10        *)
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(*									     *)
(*                   Two Left Adjoints of a Functor are Iso                  *)
(*									     *)
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(*									     *)
(*                     A. SAIBI	  May 95                  		     *)
(*									     *)
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Require Export Adjunction1.
Set Implicit Arguments.
Unset Strict Implicit.
Section ladj_iso_def.
Variables (C D : Category) (G : Functor C D) (la la' : LeftAdj G).
Let F := Adjoint la.
Let F' := Adjoint la'.
Let LAdj_unit (a : D) := Unit la a.
Let LAdj_unit' (a : D) := Unit la' a.
Definition LAdj_tau_iso (a : D) := UA_iso (LAdj_unit a) (LAdj_unit' a).
Definition LAdj_tau (a : D) := Iso_mor (LAdj_tau_iso a).

(* Specifications: *)
Lemma LAdj_nt_law : NT_law LAdj_tau.
Canonical Structure LAdj_nt := Build_NT LAdj_nt_law.
Lemma LAdj_iso : NatIso F F'.
End ladj_iso_def.