Theorems · Definition · category theory

CochainComplex.mappingCone.fst

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {F G : CochainComplex C ℤ} →
        (φ : F ⟶ G) →
          [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] →
            CochainComplex.HomComplex.Cocycle (CochainComplex.mappingCone φ) F 1

The first projection from the mapping cone, as a cocycle of degree 1.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

51 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiber