Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv_hom_id_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 : ι} (f : i₀ ⟶ i₁) (n₀ n₁ : ℤ)
  (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.cyclesIsoH_inv_hom_id._auto_1) {Z : C}
  (h : (X.H n₀).obj (CategoryTheory.ComposableArrows.mk₁ f) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.toCycles (CategoryTheory.CategoryStruct.id i₀) f f ⋯ n₀)
      (CategoryTheory.CategoryStruct.comp (X.cyclesIsoH f n₀ n₁ hn₁).hom h) =
    h

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

2 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian