Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.SpectralSequence.homologyIso

{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' : κ) →
                            [X.HasSpectralSequence data] →
                              (CategoryTheory.Abelian.SpectralObject.SpectralSequence.page X data r hr).homology pq' ≅
                                (CategoryTheory.Abelian.SpectralObject.SpectralSequence.page X data r' ⋯).X pq'

The homology of the differentials on a page of the spectral sequence identifies to the objects on the next page.

Defined in

Mathlib.Algebra.Homology.SpectralObject.SpectralSequence

Cited by

0 results in Mathlib

Foundations

Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianPreorderCategoryTheory.Abelian.SpectralObject.HasSpectralSequence