Theorems · Definition · category theory

CategoryTheory.ObjectProperty.tStructure

{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] → CategoryTheory.Triangulated.TStructure P.FullSubcategory

The t-structure induced on a full subcategory.

Defined in

Mathlib.CategoryTheory.Triangulated.TStructure.Induced

Cited by

3 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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