helm/software/matita/library/formal_topology/basic_pairs_to_basic_topologies.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "formal_topology/basic_pairs_to_o-basic_pairs.ma".
  16 include "formal_topology/o-basic_pairs_to_o-basic_topologies.ma".
  17 include "formal_topology/basic_pairs.ma".
  18 include "formal_topology/basic_topologies.ma".
  19
  20 definition basic_topology_of_basic_pair: basic_pair → basic_topology.
  21  intro bp;
  22  letin obp ≝ (o_basic_pair_of_basic_pair bp);
  23  letin obt ≝ (o_basic_topology_of_o_basic_pair obp);
  24  constructor 1;
  25   [ apply (form bp);
  26   | apply (oA obt);
  27   | apply (oJ obt);
  28   | apply (oA_is_saturation obt);
  29   | apply (oJ_is_reduction obt);
  30   | apply (Ocompatibility obt); ]
  31 qed.
  32
  33 definition continuous_relation_of_relation_pair:
  34  ∀BP1,BP2.relation_pair BP1 BP2 →
  35   continuous_relation (basic_topology_of_basic_pair BP1) (basic_topology_of_basic_pair BP2).
  36  intros (BP1 BP2 rp);
  37  letin orp ≝ (o_relation_pair_of_relation_pair ?? rp);
  38  letin ocr ≝ (o_continuous_relation_of_o_relation_pair ?? orp);
  39  constructor 1;
  40   [ apply (rp \sub \f);
  41   | apply (Oreduced ?? ocr);
  42   | apply (Osaturated ?? ocr); ]
  43 qed.
  44
  45 alias symbol "compose" (instance 3) = "category1 composition".
  46 alias symbol "compose" (instance 3) = "category1 composition".
  47 record functor1 (C1: category1) (C2: category1) : Type2 ≝
  48  { map_objs1:1> C1 → C2;
  49    map_arrows1: ∀S,T. unary_morphism1 (arrows1 ? S T) (arrows1 ? (map_objs1 S) (map_objs1 T));
  50    respects_id1: ∀o:C1. map_arrows1 ?? (id1 ? o) =_1 id1 ? (map_objs1 o);
  51    respects_comp1:
  52      ∀o1,o2,o3.∀f1:arrows1 ? o1 o2.∀f2:arrows1 ? o2 o3.
  53      map_arrows1 ?? (f2 ∘ f1) =_1 map_arrows1 ?? f2 ∘ map_arrows1 ?? f1}.
  54
  55 (*
  56 definition BTop_of_BP: functor1 BP BTop.
  57  lapply OR as F;
  58  constructor 1;
  59   [ apply basic_topology_of_basic_pair
  60   | intros; constructor 1 [ apply continuous_relation_of_relation_pair; ]
  61   | simplify; intro;
  62   ]
  63 qed.
  64 *)