Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.ccSc

{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] →
            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) →
                          κ →
                            (pq' : κ) →
                              (i₀ i₁ i₂ i₃ i₃' : ι) →
                                i₀ = data.i₀ r pq' ⋯ →
                                  i₁ = data.i₁ pq' →
                                    i₂ = data.i₂ pq' →
                                      i₃ = data.i₃ r pq' ⋯ →
                                        i₃' = data.i₃ r' pq' ⋯ →
                                          (n₀ n₁ n₂ : ℤ) →
                                            n₁ = data.deg pq' →
                                              autoParam (n₀ + 1 = n₁)
                                                  CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.ccSc._auto_1 →
                                                autoParam (n₁ + 1 = n₂)
                                                    CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.ccSc._auto_3 →
                                                  CategoryTheory.ShortComplex C

The (exact) short complex attached to the cokernel cofork cc.

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