Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.distinguished_cocone_triangle

∀ {C : Type u} {inst : CategoryTheory.Category.{v, u} C} {inst_1 : CategoryTheory.Limits.HasZeroObject C}
  {inst_2 : CategoryTheory.HasShift C ℤ} {inst_3 : CategoryTheory.Preadditive C}
  {inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive} [self : CategoryTheory.Pretriangulated C] {X Y : C}
  (f : X ⟶ Y),
  ∃ Z g h, CategoryTheory.Pretriangulated.Triangle.mk f g h ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

any morphism X ⟶ Y is part of a distinguished triangle X ⟶ Y ⟶ Z ⟶ X⟦1⟧

Defined in

Mathlib.CategoryTheory.Triangulated.Pretriangulated

Cited by

20 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Pretriangulated