Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sequence

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      [inst_1 : CategoryTheory.HasWeakSheafify J (Type v)] →
        [inst_2 : CategoryTheory.HasSheafify J AddCommGrpCat] →
          [CategoryTheory.HasExt (CategoryTheory.Sheaf J AddCommGrpCat)] →
            J.MayerVietorisSquare →
              CategoryTheory.Sheaf J AddCommGrpCat →
                (n₀ n₁ : ℕ) → n₀ + 1 = n₁ → CategoryTheory.ComposableArrows AddCommGrpCat 5

The Mayer-Vietoris long exact sequence of an abelian sheaf F : Sheaf J AddCommGrpCat for a Mayer-Vietoris square S : J.MayerVietorisSquare.

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.MayerVietoris

Cited by

1 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasSheafifyCategoryTheory.HasExt