Theorems · Definition · category theory

CochainComplex.mappingCone.map

{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) →
                  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 commutative square.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated

Cited by

19 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproducts