Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyMapData.op

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S₁ S₂ : CategoryTheory.ShortComplex C} →
        {φ : S₁ ⟶ S₂} →
          {h₁ : S₁.HomologyData} →
            {h₂ : S₂.HomologyData} →
              CategoryTheory.ShortComplex.HomologyMapData φ h₁ h₂ →
                CategoryTheory.ShortComplex.HomologyMapData (CategoryTheory.ShortComplex.opMap φ) h₂.op h₁.op

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

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

4 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms