Theorems · Definition · category theory

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.sequenceIso

{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] →
          [inst_3 : CategoryTheory.HasExt (CategoryTheory.Sheaf J AddCommGrpCat)] →
            (S : J.MayerVietorisSquare) →
              (F : CategoryTheory.Sheaf J AddCommGrpCat) →
                (n₀ n₁ : ℕ) →
                  (h : n₀ + 1 = n₁) →
                    S.sequence F n₀ n₁ h ≅ CategoryTheory.Abelian.Ext.contravariantSequence ⋯ F n₀ n₁ ⋯

Comparison isomorphism from the Mayer-Vietoris sequence and the contravariant sequence of Ext-groups.

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.MayerVietoris

Cited by

1 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasSheafifyCategoryTheory.HasExt