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(* 02110-1301 USA                                                     *)
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(*          Projet Coq - Calculus of Inductive Constructions V5.10           *)
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(*                                                                           *)
(*          Category Theory : Dual Functor                                   *)
(*                                                                           *)
(*          Amokrane Saibi May 1994                                          *)
(*                                                                           *)
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Require Export Dual.
Require Export Functor.
Set Implicit Arguments.
Unset Strict Implicit.
Section dfunctor_def.
Variables (A B : Category) (F : Functor A B).
Definition DFunctor_ob : Dual A -> Dual B := fun a : A => F a.
Definition DFunctor_map (b a : A) := FMap F a b.

(* Specifications: *)
Lemma DFunctor_comp_law : Fcomp_law (FOb:=DFunctor_ob) DFunctor_map.
Lemma DFunctor_id_law : Fid_law (FOb:=DFunctor_ob) DFunctor_map.
Canonical Structure Dfunctor :=
Build_Functor DFunctor_comp_law DFunctor_id_law.