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Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.zero

∀ {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 Y : C} (f : X ⟶ Y) (n₀ n₁ : ℤ),
  autoParam (n₀ < n₁) CategoryTheory.Triangulated.TStructure.zero._auto_1 → ∀ [t.IsLE X n₀] [t.IsGE Y n₁], f = 0
Defined in
Mathlib.CategoryTheory.Triangulated.TStructure.Basic
Cited by
7 results in Mathlib
Foundations
Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.Triangulated.TStructure.IsLECategoryTheory.Triangulated.TStructure.IsGE
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Around this declaration

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CategoryTheory.Triangulated.TStructure.zero_of_isLE_of_isGE · cited by 7TStructure.zero_of_isLE_o…CategoryTheory.Triangulated.TStructure.isGE₂ · cited by 1TStructure.isGE₂CategoryTheory.Triangulated.TStructure.isLE₂ · cited by 1TStructure.isLE₂CategoryTheory.Triangulated.TStructure.triangle_map_exists · cited by 1TStructure.triangle_map_e…CategoryTheory.Triangulated.TStructure.isGE_iff_orthogonal · cited by 1TStructure.isGE_iff_ortho…CategoryTheory.Triangulated.TStructure.isLE_iff_orthogonal · cited by 1TStructure.isLE_iff_ortho…CategoryTheory.Triangulated.TStructure.isZero · cited by 0TStructure.isZeroCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Preadditive · cited by 3309CategoryTheory.Preadditiveadd_zero · cited by 2707add_zeroCategoryTheory.shiftFunctor · cited by 1553CategoryTheory.shiftFunct…CategoryTheory.HasShift · cited by 1527CategoryTheory.HasShiftCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.Functor.Additive · cited by 1179Functor.AdditiveCategoryTheory.Pretriangulated · cited by 669CategoryTheory.Pretriangu…CategoryTheory.Triangulated.TStructure · cited by 318Triangulated.TStructureCategoryTheory.Functor.map_injective · cited by 91Functor.map_injectiveCategoryTheory.Functor.map_zero · cited by 85Functor.map_zeroCategoryTheory.Triangulated.TStructure.IsGE · cited by 48TStructure.IsGETStructure.zeroCITED BYCITES

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Cited by7

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