Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.d

{C : Type u_1} →
  {ι : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} ι] →
        [inst_2 : CategoryTheory.Abelian C] →
          (X : CategoryTheory.Abelian.SpectralObject C ι) →
            {i₀ i₁ i₂ i₃ i₄ i₅ : ι} →
              (f₁ : i₀ ⟶ i₁) →
                (f₂ : i₁ ⟶ i₂) →
                  (f₃ : i₂ ⟶ i₃) →
                    (f₄ : i₃ ⟶ i₄) →
                      (f₅ : i₄ ⟶ i₅) →
                        (n₀ n₁ n₂ n₃ : ℤ) →
                          (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.d._auto_1) →
                            (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.d._auto_3) →
                              (hn₃ : autoParam (n₂ + 1 = n₃) CategoryTheory.Abelian.SpectralObject.d._auto_5) →
                                X.E f₃ f₄ f₅ n₀ n₁ n₂ hn₁ hn₂ ⟶ X.E f₁ f₂ f₃ n₁ n₂ n₃ hn₂ hn₃

The differential E^{n}(f₃, f₄, f₅) ⟶ E^{n+1}(f₁, f₂, f₃) that is attached to a family of five composable morphisms f₁, f₂, f₃, f₄, f₅.

Defined in

Mathlib.Algebra.Homology.SpectralObject.Differentials

Cited by

28 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian