Theorems · Theorem · algebraic geometry

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.shortComplex_f

∀ {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]
  (S : J.MayerVietorisSquare),
  S.shortComplex.f =
    CategoryTheory.Limits.biprod.lift
      ((CategoryTheory.presheafToSheaf J AddCommGrpCat).map
        (CategoryTheory.Functor.whiskerRight (CategoryTheory.yoneda.map S.f₁₂) AddCommGrpCat.free))
      (-(CategoryTheory.presheafToSheaf J AddCommGrpCat).map
          (CategoryTheory.Functor.whiskerRight (CategoryTheory.yoneda.map S.f₁₃) AddCommGrpCat.free))

Defined in

Mathlib.CategoryTheory.Sites.MayerVietorisSquare

Cited by

1 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasSheafify