Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.MayerVietorisSquare.biprodAddEquiv_symm_biprodIsoProd_hom_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} (x : ↑(F.H' n S.X₄)),
  CategoryTheory.Abelian.Ext.biprodAddEquiv.symm
      ((CategoryTheory.ConcreteCategory.hom ((F.H' n S.X₂).biprodIsoProd (F.H' n S.X₃)).hom)
        ((CategoryTheory.ConcreteCategory.hom (S.toBiprod F n)) x)) =
    (CategoryTheory.Abelian.Ext.mk₀ S.shortComplex.g).comp x ⋯

Defined in

Mathlib.CategoryTheory.Sites.SheafCohomology.MayerVietoris

Cited by

0 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.HasWeakSheafifyCategoryTheory.HasSheafifyCategoryTheory.HasExt