Theorems · Definition · category theory

HomologicalComplex.homologyFunctorSingleIso

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
        {ι : Type u_1} →
          [inst_3 : DecidableEq ι] →
            (c : ComplexShape ι) →
              (j : ι) →
                [inst_4 : CategoryTheory.CategoryWithHomology C] →
                  (HomologicalComplex.single C c j).comp (HomologicalComplex.homologyFunctor C c j) ≅
                    CategoryTheory.Functor.id C

The computation of the homology of single complexes, as a natural isomorphism single C c j ⋙ homologyFunctor C c j ≅ 𝟭 C.

Defined in

Mathlib.Algebra.Homology.SingleHomology

Cited by

2 results in Mathlib

Foundations

Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEqCategoryTheory.CategoryWithHomology