Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.p_opcyclesIso_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) {i j k l : ι} (f₁ : i ⟶ j) (f₂ : j ⟶ k) (f₃ : k ⟶ l) (n₀ n₁ n₂ : ℤ)
  (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.p_opcyclesIso_hom._auto_1)
  (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.p_opcyclesIso_hom._auto_3) {Z : C}
  (h : X.opcycles f₂ f₃ n₁ ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.shortComplex f₁ f₂ f₃ n₀ n₁ n₂ hn₁ hn₂).pOpcycles
      (CategoryTheory.CategoryStruct.comp (X.opcyclesIso f₁ f₂ f₃ n₀ n₁ n₂ hn₁ hn₂).hom h) =
    CategoryTheory.CategoryStruct.comp (X.pOpcycles f₂ f₃ n₁) h

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

2 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian