Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.descE

{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) →
            {i j k l : ι} →
              (f₁ : i ⟶ j) →
                (f₂ : j ⟶ k) →
                  (f₃ : k ⟶ l) →
                    (f₁₂ : i ⟶ k) →
                      (h₁₂ : CategoryTheory.CategoryStruct.comp f₁ f₂ = f₁₂) →
                        (n₀ n₁ n₂ : ℤ) →
                          {A : C} →
                            (x : (X.H n₁).obj (CategoryTheory.ComposableArrows.mk₁ f₁₂) ⟶ A) →
                              CategoryTheory.CategoryStruct.comp
                                    ((X.H n₁).map (CategoryTheory.ComposableArrows.twoδ₂Toδ₁ f₁ f₂ f₁₂ h₁₂)) x =
                                  0 →
                                (hn₁ : n₀ + 1 = n₁) →
                                  CategoryTheory.CategoryStruct.comp (X.δ f₁₂ f₃ n₀ n₁ hn₁) x = 0 →
                                    (hn₂ :
                                        autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.descE._auto_1) →
                                      X.E f₁ f₂ f₃ n₀ n₁ n₂ hn₁ hn₂ ⟶ A

Constructor for morphisms for E^{n₁}(f₁, f₂, f₃).

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

3 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian