Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.ge_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]
  (self : CategoryTheory.Triangulated.TStructure C) (n a n' : ℤ),
  a + n' = n → ∀ (X : C), self.ge n X → self.ge n' ((CategoryTheory.shiftFunctor C a).obj X)

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Basic

Cited by

3 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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