Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyMapData.smul

{R : Type u_1} →
  {C : Type u_2} →
    [inst : Semiring R] →
      [inst_1 : CategoryTheory.Category.{v_1, u_2} C] →
        [inst_2 : CategoryTheory.Preadditive C] →
          [inst_3 : CategoryTheory.Linear R C] →
            {S₁ S₂ : CategoryTheory.ShortComplex C} →
              {φ : S₁ ⟶ S₂} →
                {h₁ : S₁.HomologyData} →
                  {h₂ : S₂.HomologyData} →
                    CategoryTheory.ShortComplex.HomologyMapData φ h₁ h₂ →
                      (a : R) → CategoryTheory.ShortComplex.HomologyMapData (a • φ) h₁ h₂

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

Defined in

Mathlib.Algebra.Homology.ShortComplex.Linear

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Linear