Theorems · Theorem · category theory

CategoryTheory.Pretriangulated.inv_rot_of_distTriang

∀ {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] [hC : CategoryTheory.Pretriangulated C],
  ∀ T ∈ CategoryTheory.Pretriangulated.distinguishedTriangles,
    T.invRotate ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

Given any distinguished triangle T, then we know T.inv_rotate is also distinguished.

Defined in

Mathlib.CategoryTheory.Triangulated.Pretriangulated

Cited by

23 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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