Theorems · Theorem · category theory

CategoryTheory.Functor.isTriangulated_of_op

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.HasShift C ℤ]
  [inst_3 : CategoryTheory.HasShift D ℤ] (F : CategoryTheory.Functor C D) [inst_4 : F.CommShift ℤ]
  [inst_5 : CategoryTheory.Limits.HasZeroObject C] [inst_6 : CategoryTheory.Preadditive C]
  [inst_7 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_8 : CategoryTheory.Pretriangulated C]
  [inst_9 : CategoryTheory.Limits.HasZeroObject D] [inst_10 : CategoryTheory.Preadditive D]
  [inst_11 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor D n).Additive] [inst_12 : CategoryTheory.Pretriangulated D]
  [F.op.IsTriangulated], F.IsTriangulated

If F.op is triangulated, so is F.

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Functor

Cited by

2 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasShiftCategoryTheory.HasShiftCategoryTheory.Functor.CommShiftCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Limits.HasZeroObjectCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Functor.IsTriangulated