Theorems · Definition · category theory

CategoryTheory.ShortComplex.Homotopy.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} →
              {φ₁ φ₂ : S₁ ⟶ S₂} →
                CategoryTheory.ShortComplex.Homotopy φ₁ φ₂ →
                  (a : R) → CategoryTheory.ShortComplex.Homotopy (a • φ₁) (a • φ₂)

Homotopy between morphisms of short complexes is compatible with the scalar multiplication.

Defined in

Mathlib.Algebra.Homology.ShortComplex.Linear

Cited by

4 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

SemiringCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Linear