Theorems · Definition · category theory

HomologicalComplex.opcyclesOpIso

{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] →
          (K : HomologicalComplex V c) →
            (i : ι) → [inst_2 : K.HasHomology i] → K.op.opcycles i ≅ Opposite.op (K.cycles i)

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

Defined in

Mathlib.Algebra.Homology.Opposite

Cited by

8 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology