Theorems · Definition · category theory

CategoryTheory.Pretriangulated.Opposite.distinguishedTriangles

(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] →
            [CategoryTheory.Pretriangulated C] → Set (CategoryTheory.Pretriangulated.Triangle Cᵒᵖ)

A triangle in Cᵒᵖ shall be distinguished iff it corresponds to a distinguished triangle in C via the equivalence triangleOpEquivalence C : (Triangle C)ᵒᵖ ≌ Triangle Cᵒᵖ.

Defined in

Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated

Cited by

7 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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