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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 : Hom Functors                                   *)
(*                                                                           *)
(*          Amokrane Saibi May 1994                                          *)
(*                                                                           *)
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Require Export SET.
Require Export Functor.
Require Export Dual.
Set Implicit Arguments.
Unset Strict Implicit.
(* 1. Hom-Functor : C(a,-) : C-->SET *)
Section funset.
Variables (C : Category) (a : C).
(* to each object b of C, we associate Hom(a,b), a object of SET *)
Definition FunSET_ob (b : C) := a --> b.
Section funset_map_def.
Variable b c : C.
Section funset_mor_def.
Variable f : b --> c.
Definition FunSET_mor1 (g : a --> b) := g o f.

Lemma FunSET_map_law1 : Map_law FunSET_mor1.
Canonical Structure FunSET_mor : Map (FunSET_ob b) (FunSET_ob c) :=
FunSET_map_law1.