Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.mem_distTriang_op_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.HasShift C ℤ]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.Preadditive C]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  (T : CategoryTheory.Pretriangulated.Triangle Cᵒᵖ),
  T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles ↔
    Opposite.unop ((CategoryTheory.Pretriangulated.triangleOpEquivalence C).inverse.obj T) ∈
      CategoryTheory.Pretriangulated.distinguishedTriangles

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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