Quellcode-Bibliothek

^© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: HoTT_coq_061.v Sprache: Coq

Original von: Coq^©

Require Import TestSuite.admit.
(* There are some problems in materialize_evar with local definitions,
   as CO below; this is not completely sorted out yet, but at least
   it fails in a smooth way at the time of today [HH] *)

(* File reduced by coq-bug-finder from 9039 lines to 7786 lines, then
   from 7245 lines to 476 lines, then from 417 lines to 249 lines,
   then from 171 lines to 127 lines. *)

Set Implicit Arguments.
Set Universe Polymorphism.
Definition admit {T} : T.
Admitted.
Delimit Scope object_scope with object.
Delimit Scope morphism_scope with morphism.
Delimit Scope category_scope with category.
Delimit Scope functor_scope with functor.
Delimit Scope natural_transformation_scope with natural_transformation.
Reserved Infix "o" (at level 40, left associativity).
Inductive paths {A : Type} (a : A) : A -> Type :=
  idpath : paths a a.

Arguments idpath {A a} , [A] a.
Notation "x = y :> A" := (@paths A x y) : type_scope.
Notation "x = y" := (x = y :>_) : type_scope.
Definition inverse {A : Type} {x y : A} (p : x = y) : y = x
  := match p with idpath => idpath end.

Record PreCategory :=
  {
    Object :> Type;
    Morphism : Object -> Object -> Type;

    Compose : forall s d d', Morphism d d' -> Morphism s d -> Morphism s d' where "f 'o' g" := (Compose f g)
  }.
Bind Scope category_scope with PreCategory.

Arguments Compose [!C%category s%object d%object d'%object] m1%morphism m2%morphism : rename.

Infix "o" := Compose : morphism_scope.
Local Open Scope morphism_scope.

Record Functor (C D : PreCategory) :=
  {
    ObjectOf :> C -> D;
    MorphismOf : forall s d, C.(Morphism) s d -> D.(Morphism) (ObjectOf s) (ObjectOf d);
    FCompositionOf : forall s d d' (m1 : C.(Morphism) s d) (m2: C.(Morphism) d d'),
                       MorphismOf _ _ (m2 o m1) = (MorphismOf _ _ m2) o (MorphismOf _ _ m1)
  }.

Bind Scope functor_scope with Functor.

Arguments MorphismOf [C%category] [D%category] F%functor [s%object d%object] m%morphism : rename, simpl nomatch.

Definition ComposeFunctors C D E
           (G : Functor D E) (F : Functor C D) : Functor C E
  := Build_Functor C E
                   (fun c => G (F c))
                   admit
                   admit.

Infix "o" := ComposeFunctors : functor_scope.

Record NaturalTransformation C D (F G : Functor C D) :=
  {
    ComponentsOf :> forall c, D.(Morphism) (F c) (G c);
    Commutes : forall s d (m : C.(Morphism) s d),
                 ComponentsOf d o F.(MorphismOf) m = G.(MorphismOf) m o ComponentsOf s
  }.

Generalizable All Variables.

Section NTComposeT.

  Variable C : PreCategory.
  Variable D : PreCategory.

  Variables F F' F'' : Functor C D.

  Variable T' : NaturalTransformation F' F''.
  Variable T : NaturalTransformation F F'.
  Let CO := fun c => T' c o T c.
  Definition NTComposeT_Commutes s d (m : Morphism C s d)
  : CO d o MorphismOf F m = MorphismOf F'' m o CO s.

    admit.
  Defined.
  Definition NTComposeT
  : NaturalTransformation F F''
    := Build_NaturalTransformation F F''
                                   (fun c => T' c o T c)
                                   NTComposeT_Commutes.
End NTComposeT.
Definition NTWhiskerR C D E (F F' : Functor D E) (T : NaturalTransformation F F')
           (G : Functor C D)
  := Build_NaturalTransformation (F o G) (F' o G)
                                 (fun c => T (G c))
                                 admit.
Class NTC_Composable A B (a : A) (b : B) (T : Type) (term : T) := {}.

Definition NTC_Composable_term `{@NTC_Composable A B a b T term} := term.
Notation "T 'o' U"
  := (@NTC_Composable_term _ _ T%natural_transformation U%natural_transformation _ _ _)
     : natural_transformation_scope.

Local Open Scope natural_transformation_scope.

Lemma NTWhiskerR_CompositionOf C D
      (F G H : Functor C D)
      (T : NaturalTransformation G H)
      (T' : NaturalTransformation F G) B (I : Functor B C)
: NTWhiskerR (NTComposeT T T') I = NTComposeT (NTWhiskerR T I) (NTWhiskerR T' I).

  admit.
Defined.
Definition FunctorCategory C D : PreCategory
  := @Build_PreCategory (Functor C D)
                        (NaturalTransformation (C := C) (D := D))
                        admit.

Notation "[ C , D ]" := (FunctorCategory C D) : category_scope.

Variable C : PreCategory.
Variable D : PreCategory.
Variable E : PreCategory.
Fail Definition NTWhiskerR_Functorial (G : [C, D]%category)
: [[D, E], [C, E]]%category
  := Build_Functor
       [C, D] [C, E]
       (fun F => F o G)
       (fun _ _ T => T o G)
       (fun _ _ _ _ _ => inverse (NTWhiskerR_CompositionOf _ _ _)).
(* Anomaly: Uncaught exception Not_found(_). Please report. *)

¤ Dauer der Verarbeitung: 0.15 Sekunden (vorverarbeitet) ¤

Download des Quellennavigators
Download des sprechenden Kalenders
in der Quellcodebibliothek suchen

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.