Theorems · Definition · category theory

CochainComplex.mappingCocone.liftCochain

{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} →
              {n m : ℤ} →
                CochainComplex.HomComplex.Cochain M K n →
                  CochainComplex.HomComplex.Cochain M L m →
                    m + 1 = n → CochainComplex.HomComplex.Cochain M (CochainComplex.mappingCocone φ) n

Constructor for cochains to mappingCocone.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone

Cited by

12 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber