Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyMapData.neg

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {S₁ S₂ : CategoryTheory.ShortComplex C} →
        {φ : S₁ ⟶ S₂} →
          {h₁ : S₁.HomologyData} →
            {h₂ : S₂.HomologyData} →
              CategoryTheory.ShortComplex.HomologyMapData φ h₁ h₂ →
                CategoryTheory.ShortComplex.HomologyMapData (-φ) h₁ h₂

Given a homology map data for a morphism φ, this is the induced homology map data for -φ.

Defined in

Mathlib.Algebra.Homology.ShortComplex.Preadditive

Cited by

2 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive