Theorems · Theorem · category theory

CategoryTheory.Abelian.SpectralObject.spectralSequenceFirstPageXIso_inv

∀ {C : Type u_1} {ι : Type u_2} {κ : Type u_3} [inst : CategoryTheory.Category.{u_4, 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 : data.HasFirstPageComputation] [inst_4 : X.HasSpectralSequence data] (pq : κ) (i₁ i₂ : ι)
  (hi₁ : i₁ = data.i₁ pq) (hi₂ : i₂ = data.i₂ pq) (n₀ n₁ n₂ : ℤ) (hn₁' : n₁ = data.deg pq)
  (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.spectralSequenceFirstPageXIso_inv._auto_1)
  (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.spectralSequenceFirstPageXIso_inv._auto_3),
  (X.spectralSequenceFirstPageXIso data pq i₁ i₂ hi₁ hi₂ n₁ hn₁').inv =
    CategoryTheory.CategoryStruct.comp (X.EIsoH (CategoryTheory.homOfLE ⋯) n₀ n₁ n₂ hn₁ hn₂).inv
      (X.spectralSequencePageXIso data r₀ ⋯ pq i₁ i₁ i₂ i₂ ⋯ hi₁ hi₂ ⋯ n₀ n₁ n₂ hn₁' ⋯ ⋯).inv

Defined in

Mathlib.Algebra.Homology.SpectralObject.FirstPage

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianPreorderCategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.HasFirstPageComputationCategoryTheory.Abelian.SpectralObject.HasSpectralSequence