Theorems · Definition · category theory

HomologicalComplex.singleObjHomologySelfIso

{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) → (A : C) → ((HomologicalComplex.single C c j).obj A).homology j ≅ A

The canonical isomorphism ((single C c j).obj A).homology j ≅ A

Defined in

Mathlib.Algebra.Homology.SingleHomology

Cited by

20 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectDecidableEq