Theorems · Theorem · category theory

HomologicalComplex.homotopyCofiber.inlX_fstX

∀ {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 j i),
  CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.inlX φ i j hij)
      (HomologicalComplex.homotopyCofiber.fstX φ j i hij) =
    CategoryTheory.CategoryStruct.id (F.X i)

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

6 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRel