Theorems · Definition · category theory

CategoryTheory.Functor.toEventualRangesSectionsEquiv

{J : Type u} →
  [inst : CategoryTheory.Category.{v_1, u} J] →
    (F : CategoryTheory.Functor J (Type v)) →
      [inst_1 : CategoryTheory.IsCofilteredOrEmpty J] → ↑F.toEventualRanges.sections ≃ ↑F.sections

The sections of the functor F : J ⥤ Type v are in bijection with the sections of F.toEventualRanges.

Defined in: Mathlib.CategoryTheory.CofilteredSystem
Cited by: 0 results in Mathlib
Foundations: Depth 21 from the axioms · uses propext, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.IsCofilteredOrEmpty

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Functorstatement and proof · cited by 16,252
Equivstatement · cited by 8,337
Set.Elemstatement and proof · cited by 7,166
CategoryTheory.Functor.sectionsstatement and proof · cited by 140
CategoryTheory.IsCofilteredOrEmptystatement and proof · cited by 55
CategoryTheory.Functor.toEventualRangesstatement and proof · cited by 4

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