Theorems · Definition · category theory

CategoryTheory.ShortComplex.LeftHomologyMapData.op

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

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

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms