Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.spectralSequencePageXIso.congr_simp

∀ {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) (i₀ i₁ i₂ i₃ : ι) (h₀ : i₀ = data.i₀ r pq ⋯)
  (h₁ : i₁ = data.i₁ pq) (h₂ : i₂ = data.i₂ pq) (h₃ : i₃ = data.i₃ r pq ⋯) (n₀ n₁ n₂ : ℤ) (h : n₁ = data.deg pq)
  (hn₁ : n₀ + 1 = n₁) (hn₂ : n₁ + 1 = n₂),
  X.spectralSequencePageXIso data r hr pq i₀ i₁ i₂ i₃ h₀ h₁ h₂ h₃ n₀ n₁ n₂ h hn₁ hn₂ =
    X.spectralSequencePageXIso data r hr pq i₀ i₁ i₂ i₃ h₀ h₁ h₂ h₃ n₀ n₁ n₂ h hn₁ hn₂

Defined in

Mathlib.Algebra.Homology.SpectralObject.FirstPage

Cited by

0 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianPreorderCategoryTheory.Abelian.SpectralObject.HasSpectralSequence