Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.shortComplexMap

{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) →
                    {i' j' k' l' : ι} →
                      (f₁' : i' ⟶ j') →
                        (f₂' : j' ⟶ k') →
                          (f₃' : k' ⟶ l') →
                            (CategoryTheory.ComposableArrows.mk₃ f₁ f₂ f₃ ⟶
                                CategoryTheory.ComposableArrows.mk₃ f₁' f₂' f₃') →
                              (n₀ n₁ n₂ : ℤ) →
                                (hn₁ :
                                    autoParam (n₀ + 1 = n₁)
                                      CategoryTheory.Abelian.SpectralObject.shortComplexMap._auto_1) →
                                  (hn₂ :
                                      autoParam (n₁ + 1 = n₂)
                                        CategoryTheory.Abelian.SpectralObject.shortComplexMap._auto_3) →
                                    X.shortComplex f₁ f₂ f₃ n₀ n₁ n₂ ⋯ ⋯ ⟶ X.shortComplex f₁' f₂' f₃' n₀ n₁ n₂ ⋯ ⋯

The functoriality of shortComplex with respect to morphisms in ComposableArrows ι 3.

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

17 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian