Theorems · Definition · category theory

CategoryTheory.Abelian.SpectralObject.homologyDataIdId

{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 : ι} →
              (f : i ⟶ j) →
                (n₀ n₁ n₂ : ℤ) →
                  (hn₁ : autoParam (n₀ + 1 = n₁) CategoryTheory.Abelian.SpectralObject.homologyDataIdId._auto_1) →
                    (hn₂ : autoParam (n₁ + 1 = n₂) CategoryTheory.Abelian.SpectralObject.homologyDataIdId._auto_3) →
                      (X.shortComplex (CategoryTheory.CategoryStruct.id i) f (CategoryTheory.CategoryStruct.id j) n₀ n₁
                          n₂ hn₁ hn₂).HomologyData

An homology data for X.shortComplex n₀ n₁ n₂ hn₁ hn₂ (𝟙 i) f (𝟙 j), expressing H^n₁(f) as the homology of this short complex, see EIsoH.

Defined in

Mathlib.Algebra.Homology.SpectralObject.Page

Cited by

15 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Abelian