Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.to_truncLT_obj_ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} 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) {n : ℤ} {Y X : C} {f₁ f₂ : Y ⟶ (t.truncLT n).obj X},
  CategoryTheory.CategoryStruct.comp f₁ ((t.truncLTι n).app X) =
      CategoryTheory.CategoryStruct.comp f₂ ((t.truncLTι n).app X) →
    ∀ [t.IsLE Y (n - 1)], f₁ = f₂

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE

Cited by

6 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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