Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.isoToPlus

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (J : CategoryTheory.GrothendieckTopology C) →
      {D : Type w} →
        [inst_1 : CategoryTheory.Category.{w', w} D] →
          [inst_2 :
              ∀ (P : CategoryTheory.Functor Cᵒᵖ D) (X : C) (S : J.Cover X),
                CategoryTheory.Limits.HasMultiequalizer (S.index P)] →
            (P : CategoryTheory.Functor Cᵒᵖ D) →
              [inst_3 : ∀ (X : C), CategoryTheory.Limits.HasColimitsOfShape (J.Cover X)ᵒᵖ D] →
                CategoryTheory.Presheaf.IsSheaf J P → (P ≅ J.plusObj P)

The natural isomorphism between P and P⁺ when P is a sheaf.

Defined in

Mathlib.CategoryTheory.Sites.Plus

Cited by

5 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasMultiequalizerCategoryTheory.Limits.HasColimitsOfShape