Theorems · Theorem · category theory

HomologicalComplex.homotopyCofiber.inr_mapHomologicalComplexObjIso_hom_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {ι : Type u_2}
  {c : ComplexShape ι} {F G : HomologicalComplex C c} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ]
  [inst_3 : DecidableRel c.Rel] {D : Type u_3} [inst_4 : CategoryTheory.Category.{v_2, u_3} D]
  [inst_5 : CategoryTheory.Preadditive D] (H : CategoryTheory.Functor C D) [inst_6 : H.Additive]
  [inst_7 : HomologicalComplex.HasHomotopyCofiber ((H.mapHomologicalComplex c).map φ)] {Z : HomologicalComplex D c}
  (h : HomologicalComplex.homotopyCofiber ((H.mapHomologicalComplex c).map φ) ⟶ Z),
  CategoryTheory.CategoryStruct.comp ((H.mapHomologicalComplex c).map (HomologicalComplex.homotopyCofiber.inr φ))
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.mapHomologicalComplexObjIso φ H).hom h) =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.inr ((H.mapHomologicalComplex c).map φ)) h

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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