Theorems · Definition · category theory

HomologicalComplex.cyclesOpNatIso

{ι : Type u_1} →
  (V : Type u_2) →
    [inst : CategoryTheory.Category.{v_1, u_2} V] →
      (c : ComplexShape ι) →
        [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] →
          [inst_2 : CategoryTheory.CategoryWithHomology V] →
            (i : ι) →
              (HomologicalComplex.opFunctor V c).comp (HomologicalComplex.cyclesFunctor Vᵒᵖ c.symm i) ≅
                (HomologicalComplex.opcyclesFunctor V c i).op

The natural isomorphism K.op.cycles i ≅ op (K.opcycles i).

Defined in

Mathlib.Algebra.Homology.Opposite

Cited by

2 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.CategoryWithHomology