Theorems · Theorem · category theory

HomologicalComplex.homotopyCofiber.d_sndX

∀ {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 : ι) (hij : c.Rel i j),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.d φ i j)
      (HomologicalComplex.homotopyCofiber.sndX φ j) =
    CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.fstX φ i j hij) (φ.f j) +
      CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.sndX φ i) (G.d i j)

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRel