Theorems · Definition · category theory

CochainComplex.mappingCone.mapOfHomotopy

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] →
        {K₁ L₁ K₂ L₂ : CochainComplex C ℤ} →
          {φ₁ : K₁ ⟶ L₁} →
            {φ₂ : K₂ ⟶ L₂} →
              {a : K₁ ⟶ K₂} →
                {b : L₁ ⟶ L₂} →
                  Homotopy (CategoryTheory.CategoryStruct.comp φ₁ b) (CategoryTheory.CategoryStruct.comp a φ₂) →
                    (CochainComplex.mappingCone φ₁ ⟶ CochainComplex.mappingCone φ₂)

The morphism mappingCone φ₁ ⟶ mappingCone φ₂ that is induced by a square that is commutative up to homotopy.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated

Cited by

7 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts