Theorems · Definition · category theory

CategoryTheory.Triangulated.TStructure.eTruncLTGEIsoGELT

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
        [inst_3 : CategoryTheory.HasShift C ℤ] →
          [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] →
            [inst_5 : CategoryTheory.Pretriangulated C] →
              (t : CategoryTheory.Triangulated.TStructure C) →
                [CategoryTheory.IsTriangulated C] →
                  (a b : EInt) → (t.eTruncGE.obj a).comp (t.eTruncLT.obj b) ≅ (t.eTruncLT.obj b).comp (t.eTruncGE.obj a)

The commutation natural isomorphism t.eTruncGE.obj a ⋙ t.eTruncLT.obj b ≅ t.eTruncLT.obj b ⋙ t.eTruncGE.obj a for all a and b in EInt.

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc

Cited by

12 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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