Theorems · Definition · category theory

CategoryTheory.ShortComplex.RightHomologyMapData.unop

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S₁ S₂ : CategoryTheory.ShortComplex Cᵒᵖ} →
        {φ : S₁ ⟶ S₂} →
          {h₁ : S₁.RightHomologyData} →
            {h₂ : S₂.RightHomologyData} →
              CategoryTheory.ShortComplex.RightHomologyMapData φ h₁ h₂ →
                CategoryTheory.ShortComplex.LeftHomologyMapData (CategoryTheory.ShortComplex.unopMap φ) h₂.unop h₁.unop

A right homology map data for a morphism of short complexes in the opposite category induces a left homology map data in the original category.

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

3 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms