Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.distinguished_cocone_triangle

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} 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] [inst_5 : CategoryTheory.Pretriangulated C]
  (P : CategoryTheory.ObjectProperty C) [P.IsTriangulatedClosed₃] {X Y : C} (a : X ⟶ Y),
  P X →
    P Y →
      ∃ Z,
        ∃ (_ : P Z),
          ∃ b c,
            CategoryTheory.Pretriangulated.Triangle.mk a b c ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

Defined in

Mathlib.CategoryTheory.Triangulated.Subcategory

Cited by

1 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.ObjectProperty.IsTriangulatedClosed₃