Theorems · Definition · category theory

HomologicalComplex.homologyFunctorIso

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {ι : Type u_2} →
        (c : ComplexShape ι) →
          (i : ι) →
            [inst_2 : CategoryTheory.CategoryWithHomology C] →
              HomologicalComplex.homologyFunctor C c i ≅
                (HomologicalComplex.shortComplexFunctor C c i).comp (CategoryTheory.ShortComplex.homologyFunctor C)

The natural isomorphism K.homology i ≅ (K.sc i).homology for all homological complexes K.

Defined in

Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex

Cited by

3 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryWithHomology