Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.opcyclesToE

{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 : ι} →
              (f₁ : i₀ ⟶ i₁) →
                (f₂ : i₁ ⟶ i₂) →
                  (f₃ : i₂ ⟶ i₃) →
                    (f₁₂ : i₀ ⟶ i₂) →
                      CategoryTheory.CategoryStruct.comp f₁ f₂ = f₁₂ →
                        (n₀ n₁ n₂ : ℤ) →
                          (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.opcyclesToE._auto_1) →
                            (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.opcyclesToE._auto_3) →
                              X.opcycles f₁₂ f₃ n₁ ⟶ X.E f₁ f₂ f₃ n₀ n₁ n₂ hn₁ hn₂

The map opZ^n(f₁ ≫ f₂, f₃) ⟶ E^n(f₁, f₂, f₃).

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

13 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian