Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.descE.congr_simp

∀ {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) {i j k l : ι} (f₁ : i ⟶ j) (f₂ : j ⟶ k) (f₃ : k ⟶ l) (f₁₂ : i ⟶ k)
  (h₁₂ : CategoryTheory.CategoryStruct.comp f₁ f₂ = f₁₂) (n₀ n₁ n₂ : ℤ) {A : C}
  (x x_1 : (X.H n₁).obj (CategoryTheory.ComposableArrows.mk₁ f₁₂) ⟶ A) (e_x : x = x_1)
  (h :
    CategoryTheory.CategoryStruct.comp ((X.H n₁).map (CategoryTheory.ComposableArrows.twoδ₂Toδ₁ f₁ f₂ f₁₂ h₁₂)) x = 0)
  (hn₁ : n₀ + 1 = n₁) (h' : CategoryTheory.CategoryStruct.comp (X.δ f₁₂ f₃ n₀ n₁ hn₁) x = 0) (hn₂ : n₁ + 1 = n₂),
  X.descE f₁ f₂ f₃ f₁₂ h₁₂ n₀ n₁ n₂ x h hn₁ h' hn₂ = X.descE f₁ f₂ f₃ f₁₂ h₁₂ n₀ n₁ n₂ x_1 ⋯ hn₁ ⋯ hn₂

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

1 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian