Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.dHomologyData_left_i

∀ {C : Type u_1} {ι : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.Category.{v_2, u_2} ι] (X : CategoryTheory.Abelian.SpectralObject C ι)
  {i₀ i₁ i₂ i₃ i₄ i₅ i₆ i₇ : ι} (f₁ : i₀ ⟶ i₁) (f₂ : i₁ ⟶ i₂) (f₃ : i₂ ⟶ i₃) (f₄ : i₃ ⟶ i₄) (f₅ : i₄ ⟶ i₅)
  (f₆ : i₅ ⟶ i₆) (f₇ : i₆ ⟶ i₇) (f₂₃ : i₁ ⟶ i₃) (h₂₃ : CategoryTheory.CategoryStruct.comp f₂ f₃ = f₂₃) (f₅₆ : i₄ ⟶ i₆)
  (h₅₆ : CategoryTheory.CategoryStruct.comp f₅ f₆ = f₅₆) (n₀ n₁ n₂ n₃ n₄ : ℤ)
  (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.dHomologyData._auto_1)
  (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.dHomologyData._auto_3)
  (hn₃ : autoParam (n₂ + 1 = n₃) CategoryTheory.Abelian.SpectralObject.dHomologyData._auto_5)
  (hn₄ : autoParam (n₃ + 1 = n₄) CategoryTheory.Abelian.SpectralObject.dHomologyData._auto_7),
  (X.dHomologyData f₁ f₂ f₃ f₄ f₅ f₆ f₇ f₂₃ h₂₃ f₅₆ h₅₆ n₀ n₁ n₂ n₃ n₄ hn₁ hn₂ hn₃ hn₄).left.i =
    X.map f₂₃ f₄ f₅ f₃ f₄ f₅ (CategoryTheory.ComposableArrows.fourδ₁Toδ₀ f₂ f₃ f₄ f₅ f₂₃ h₂₃) n₁ n₂ n₃ ⋯ ⋯

Defined in

Mathlib.Algebra.Homology.SpectralObject.Homology

Cited by

0 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Category