Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kfSc_exact

∀ {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)
  (r r' : ℤ) (hrr' : r + 1 = r') (hr : r₀ ≤ r) (pq' pq'' : κ),
  (c r).next pq' = pq'' →
    ∀ (i₀' i₀ i₁ i₂ i₃ : ι) (hi₀' : i₀' = data.i₀ r' pq' ⋯) (hi₀ : i₀ = data.i₀ r pq' ⋯) (hi₁ : i₁ = data.i₁ pq')
      (hi₂ : i₂ = data.i₂ pq') (hi₃ : i₃ = data.i₃ r pq' ⋯) (n₀ n₁ n₂ : ℤ) (hn₁' : n₁ = data.deg pq')
      [X.HasSpectralSequence data]
      (hn₁ :
        autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kfSc_exact._auto_1)
      (hn₂ :
        autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kfSc_exact._auto_3),
      (CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kfSc X data r r' hrr' hr pq' pq'' i₀' i₀ i₁
          i₂ i₃ hi₀' hi₀ hi₁ hi₂ hi₃ n₀ n₁ n₂ hn₁' hn₁ hn₂).Exact

Defined in

Mathlib.Algebra.Homology.SpectralObject.SpectralSequence

Cited by

0 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianPreorderCategoryTheory.Abelian.SpectralObject.HasSpectralSequence