Theorems · Definition · category theory

CochainComplex.mappingCocone.lift

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {K L : CochainComplex C ℤ} →
        (φ : K ⟶ L) →
          [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] →
            {M : CochainComplex C ℤ} →
              (α : M ⟶ K) →
                (β : CochainComplex.HomComplex.Cochain M L (-1)) →
                  CochainComplex.HomComplex.δ (-1) 0 β +
                        CochainComplex.HomComplex.Cochain.ofHom (CategoryTheory.CategoryStruct.comp α φ) =
                      0 →
                    (M ⟶ CochainComplex.mappingCocone φ)

Constructor for morphisms to mappingCocone.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

8 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber