Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.toBiprod_apply

∀ {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) {n : ℕ} (y : ↑(F.H' n S.X₄)),
  (CategoryTheory.ConcreteCategory.hom (S.toBiprod F n)) y =
    (CategoryTheory.ConcreteCategory.hom
        (((F.cohomologyPresheaf n).obj (Opposite.op S.X₂)).biprodIsoProd
            ((F.cohomologyPresheaf n).obj (Opposite.op S.X₃))).inv)
      ((CategoryTheory.ConcreteCategory.hom ((F.cohomologyPresheaf n).map S.f₂₄.op)) y,
        (CategoryTheory.ConcreteCategory.hom ((F.cohomologyPresheaf n).map S.f₃₄.op)) y)

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