Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kf

{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) →
                            (i₀' i₀ i₁ i₂ i₃ : ι) →
                              i₀' = data.i₀ r' pq' ⋯ →
                                i₀ = data.i₀ r pq' ⋯ →
                                  i₁ = data.i₁ pq' →
                                    i₂ = data.i₂ pq' →
                                      i₃ = data.i₃ r pq' ⋯ →
                                        (n₀ n₁ n₂ : ℤ) →
                                          n₁ = data.deg pq' →
                                            autoParam (n₀ + 1 = n₁)
                                                CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kf._auto_1 →
                                              autoParam (n₁ + 1 = n₂)
                                                  CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.kf._auto_3 →
                                                CategoryTheory.Limits.KernelFork
                                                  ((CategoryTheory.Abelian.SpectralObject.SpectralSequence.page X data r
                                                        hr).d
                                                    pq' pq'')

A (limit) kernel fork of the differential on the rth page whose point identifies to an object X.E

Defined in

Mathlib.Algebra.Homology.SpectralObject.SpectralSequence

Cited by

6 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianPreorder