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||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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 obt ≝ (OR (BP_to_OBP bp));
  23  constructor 1;
  24   [ apply (form bp);
  25   | apply (oA obt);
  26   | apply (oJ obt);
  27   | apply (oA_is_saturation obt);
  28   | apply (oJ_is_reduction obt);
  29   | apply (Ocompatibility obt); ]
  30 qed.
  31
  32 definition continuous_relation_of_relation_pair:
  33  ∀BP1,BP2.relation_pair BP1 BP2 →
  34   continuous_relation (basic_topology_of_basic_pair BP1) (basic_topology_of_basic_pair BP2).
  35  intros (BP1 BP2 rp);
  36  letin ocr ≝ (OR⎽⇒ (BP_to_OBP⎽⇒ rp));
  37  constructor 1;
  38   [ apply (rp \sub \f);
  39   | apply (Oreduced ?? ocr);
  40   | apply (Osaturated ?? ocr); ]
  41 qed.
  42
  43 alias symbol "compose" (instance 3) = "category1 composition".
  44 alias symbol "compose" (instance 3) = "category1 composition".
  45 record functor1 (C1: category1) (C2: category1) : Type2 ≝
  46  { map_objs1:1> C1 → C2;
  47    map_arrows1: ∀S,T. unary_morphism1 (arrows1 ? S T) (arrows1 ? (map_objs1 S) (map_objs1 T));
  48    respects_id1: ∀o:C1. map_arrows1 ?? (id1 ? o) =_1 id1 ? (map_objs1 o);
  49    respects_comp1:
  50      ∀o1,o2,o3.∀f1:arrows1 ? o1 o2.∀f2:arrows1 ? o2 o3.
  51      map_arrows1 ?? (f2 ∘ f1) =_1 map_arrows1 ?? f2 ∘ map_arrows1 ?? f1}.
  52
  53 (*
  54 definition BTop_of_BP: functor1 BP BTop.
  55  constructor 1;
  56   [ apply basic_topology_of_basic_pair
  57   | intros; constructor 1 [ apply continuous_relation_of_relation_pair; ]
  58   | simplify; intro;
  59   ]
  60 qed.
  61
  62 lemma BBBB_faithful : failthful2 ?? VVV
  63 FIXME
  64 *)