Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.liftCycles_i_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 : ι} (f : i ⟶ j) (g : j ⟶ k) (n₀ n₁ : ℤ) (hn₁ : n₀ + 1 = n₁)
  {A : C} (x : A ⟶ (X.H n₀).obj (CategoryTheory.ComposableArrows.mk₁ g))
  (hx : CategoryTheory.CategoryStruct.comp x (X.δ f g n₀ n₁ hn₁) = 0) {Z : C}
  (h : (X.H n₀).obj (CategoryTheory.ComposableArrows.mk₁ g) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.liftCycles f g n₀ n₁ hn₁ x hx)
      (CategoryTheory.CategoryStruct.comp (X.iCycles f g n₀) h) =
    CategoryTheory.CategoryStruct.comp x h

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian