Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.isGE_of_shift

∀ {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) (X : C) (n a n' : ℤ),
  autoParam (a + n' = n) CategoryTheory.Triangulated.TStructure.isGE_of_shift._auto_1 →
    ∀ [t.IsGE ((CategoryTheory.shiftFunctor C a).obj X) n'], t.IsGE X n

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Basic

Cited by

1 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Triangulated.TStructure.IsGE