Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.isZero_spectralSequence_page_X_of_isZero_H

∀ {C : Type u_1} {ι : Type u_2} {κ : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Abelian C] [inst_2 : Preorder ι] (X : CategoryTheory.Abelian.SpectralObject C ι)
  {c : ℤ → ComplexShape κ} {r₀ : ℤ} (data : CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore ι c r₀)
  [inst_3 : X.HasSpectralSequence data] (r : ℤ) (hr : r₀ ≤ r) (pq : κ) (n : ℤ),
  n = data.deg pq →
    ∀ (i₁ i₂ : ι) (h₁ : i₁ = data.i₁ pq) (h₂ : i₂ = data.i₂ pq),
      CategoryTheory.Limits.IsZero ((X.H n).obj (CategoryTheory.ComposableArrows.mk₁ (CategoryTheory.homOfLE ⋯))) →
        CategoryTheory.Limits.IsZero (((X.spectralSequence data).page r ⋯).X pq)

Defined in

Mathlib.Algebra.Homology.SpectralObject.SpectralSequence

Cited by

1 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianPreorderCategoryTheory.Abelian.SpectralObject.HasSpectralSequence