Theorems · Theorem · category theory

CochainComplex.mappingCone.map_inr

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v, u_1} C]
  [inst_1 : CategoryTheory.Category.{v', u_2} D] [inst_2 : CategoryTheory.Preadditive C]
  [inst_3 : CategoryTheory.Preadditive D] {F G : CochainComplex C ℤ} (φ : F ⟶ G)
  [inst_4 : HomologicalComplex.HasHomotopyCofiber φ] (H : CategoryTheory.Functor C D) [inst_5 : H.Additive]
  [inst_6 : HomologicalComplex.HasHomotopyCofiber ((H.mapHomologicalComplex (ComplexShape.up ℤ)).map φ)],
  CategoryTheory.CategoryStruct.comp
      ((H.mapHomologicalComplex (ComplexShape.up ℤ)).map (CochainComplex.mappingCone.inr φ))
      (CochainComplex.mappingCone.mapHomologicalComplexIso φ H).hom =
    CochainComplex.mappingCone.inr ((H.mapHomologicalComplex (ComplexShape.up ℤ)).map φ)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.MappingCone

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberCategoryTheory.Functor.AdditiveHomologicalComplex.HasHomotopyCofiber