Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.tStructure_isLE_iff

∀ {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]
  (P : CategoryTheory.ObjectProperty C) (t : CategoryTheory.Triangulated.TStructure C) [inst_6 : P.IsTriangulated]
  [h : P.HasInducedTStructure t] (X : P.FullSubcategory) (n : ℤ), (P.tStructure t).IsLE X n ↔ t.IsLE X.obj n

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Induced

Cited by

1 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObjectCategoryTheory.HasShiftCategoryTheory.Functor.AdditiveCategoryTheory.PretriangulatedCategoryTheory.ObjectProperty.IsTriangulatedCategoryTheory.ObjectProperty.HasInducedTStructure