Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.p_opcyclesToE_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 i₃ : ι} (f₁ : i₀ ⟶ i₁) (f₂ : i₁ ⟶ i₂) (f₃ : i₂ ⟶ i₃)
  (f₁₂ : i₀ ⟶ i₂) (h₁₂ : CategoryTheory.CategoryStruct.comp f₁ f₂ = f₁₂) (n₀ n₁ n₂ : ℤ)
  (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.p_opcyclesToE._auto_1)
  (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.p_opcyclesToE._auto_3) {Z : C}
  (h : X.E f₁ f₂ f₃ n₀ n₁ n₂ hn₁ hn₂ ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.pOpcycles f₁₂ f₃ n₁)
      (CategoryTheory.CategoryStruct.comp (X.opcyclesToE f₁ f₂ f₃ f₁₂ h₁₂ n₀ n₁ n₂ hn₁ hn₂) h) =
    CategoryTheory.CategoryStruct.comp (X.toCycles f₁ f₂ f₁₂ h₁₂ n₁)
      (CategoryTheory.CategoryStruct.comp (X.πE f₁ f₂ f₃ n₀ n₁ n₂ hn₁ hn₂) h)

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

2 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian