Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.trW_iff

∀ {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) {X Y : C} (f : X ⟶ Y),
  P.trW f ↔
    ∃ Z g h,
      ∃ (_ : CategoryTheory.Pretriangulated.Triangle.mk f g h ∈ CategoryTheory.Pretriangulated.distinguishedTriangles),
        P Z

Defined in

Mathlib.CategoryTheory.Triangulated.Subcategory

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Pretriangulated