Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.isGE_of_ge

∀ {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) (p q : ℤ),
  autoParam (p ≤ q) CategoryTheory.Triangulated.TStructure.isGE_of_ge._auto_1 → ∀ [t.IsGE X q], t.IsGE X p

Defined in: Mathlib.CategoryTheory.Triangulated.TStructure.Basic
Cited by: 6 results in Mathlib
Foundations: Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasZeroObject CategoryTheory.HasShift CategoryTheory.Functor.Additive CategoryTheory.Pretriangulated CategoryTheory.Triangulated.TStructure.IsGE

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
CategoryTheory.HasShiftstatement and proof · cited by 1,527
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
CategoryTheory.Pretriangulatedstatement and proof · cited by 669
CategoryTheory.Triangulated.TStructurestatement and proof · cited by 318
CategoryTheory.Triangulated.TStructure.IsGEstatement and proof · cited by 48
CategoryTheory.Triangulated.TStructure.ge_of_isGEproof · cited by 5
CategoryTheory.Triangulated.TStructure.ge_antitoneproof · cited by 1

Cited by6

Results whose statement or proof uses this declaration.

CategoryTheory.Triangulated.TStructure.zeroproof · cited by 7
CategoryTheory.Triangulated.TStructure.isIso_truncLT_map_truncLTι_appproof · cited by 3
CategoryTheory.Triangulated.TStructure.isGE_truncGE_objproof · cited by 1
CategoryTheory.Triangulated.TStructure.isGE_eTruncGE_obj_objproof · cited by 0
CategoryTheory.Triangulated.TStructure.isZero_eTruncLT_obj_objproof · cited by 0
CategoryTheory.Triangulated.TStructure.isGE_of_GEproof · cited by 0