Theorems · Definition · algebraic geometry

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      [inst_1 : CategoryTheory.HasWeakSheafify J (Type v)] →
        [CategoryTheory.HasSheafify J AddCommGrpCat] →
          J.MayerVietorisSquare → CategoryTheory.ShortComplex (CategoryTheory.Sheaf J AddCommGrpCat)

The short complex of abelian sheaves ℤ[S.X₁] ⟶ ℤ[S.X₂] ⊞ ℤ[S.X₃] ⟶ ℤ[S.X₄] where the left map is a difference and the right map a sum.

Defined in

Mathlib.CategoryTheory.Sites.MayerVietorisSquare

Cited by

9 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasSheafify