Theorems · Theorem · category theory

HomologicalComplex.homotopyCofiber.inlX_d_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] (i j k : ι) (hij : c.Rel i j) (hjk : c.Rel j k) {Z : C}
  (h : HomologicalComplex.homotopyCofiber.X φ j ⟶ Z),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.inlX φ j i hij)
      (CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.d φ i j) h) =
    CategoryTheory.CategoryStruct.comp
      (-CategoryTheory.CategoryStruct.comp (F.d j k) (HomologicalComplex.homotopyCofiber.inlX φ k j hjk) +
        CategoryTheory.CategoryStruct.comp (φ.f j) (HomologicalComplex.homotopyCofiber.inrX φ j))
      h

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRel