Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom_assoc

∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} ι] [inst_2 : CategoryTheory.Abelian C]
  (X : CategoryTheory.Abelian.SpectralObject C ι) {i₀ i₁ i₂ : ι} (f₁ : i₀ ⟶ i₁) (f₂ : i₁ ⟶ i₂) (n₀ n₁ n₂ n₃ : ℤ)
  (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom._auto_1)
  (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom._auto_3)
  (hn₃ : autoParam (n₂ + 1 = n₃) CategoryTheory.Abelian.SpectralObject.d_EIsoH_hom._auto_5) {Z : C}
  (h : (X.H n₂).obj (CategoryTheory.ComposableArrows.mk₁ f₁) ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (X.d (CategoryTheory.CategoryStruct.id i₀) f₁ (CategoryTheory.CategoryStruct.id i₁) f₂
        (CategoryTheory.CategoryStruct.id i₂) n₀ n₁ n₂ n₃ hn₁ hn₂ hn₃)
      (CategoryTheory.CategoryStruct.comp (X.EIsoH f₁ n₁ n₂ n₃ hn₂ hn₃).hom h) =
    CategoryTheory.CategoryStruct.comp (X.EIsoH f₂ n₀ n₁ n₂ hn₁ hn₂).hom
      (CategoryTheory.CategoryStruct.comp (X.δ f₁ f₂ n₁ n₂ hn₂) h)

Defined in

Mathlib.Algebra.Homology.SpectralObject.Differentials

Cited by

1 results in Mathlib

Foundations

Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian