Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.liftOpcycles_fromOpcycles_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) (fg : i ⟶ k)
  (h : CategoryTheory.CategoryStruct.comp f g = fg) {A : C} {n : ℤ}
  (x : A ⟶ (X.H n).obj (CategoryTheory.ComposableArrows.mk₁ fg))
  (hx : CategoryTheory.CategoryStruct.comp x ((X.H n).map (CategoryTheory.ComposableArrows.twoδ₁Toδ₀ f g fg h)) = 0)
  {Z : C} (h_1 : (X.H n).obj (CategoryTheory.ComposableArrows.mk₁ fg) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (X.liftOpcycles f g fg h x hx)
      (CategoryTheory.CategoryStruct.comp (X.fromOpcycles f g fg h n) h_1) =
    CategoryTheory.CategoryStruct.comp x h_1

Defined in

Mathlib.Algebra.Homology.SpectralObject.Cycles

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian