Theorems · Definition · category theory

HomologicalComplex.homotopyCofiber.XIso

{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 : ι) → ¬c.Rel i (c.next i) → (HomologicalComplex.homotopyCofiber.X φ i ≅ G.X i)

The canonical isomorphism (homotopyCofiber φ).X i ≅ G.X i when ¬ c.Rel i (c.next i).

Defined in

Mathlib.Algebra.Homology.HomotopyCofiber

Cited by

13 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveHomologicalComplex.HasHomotopyCofiberDecidableRel