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Theorems · Definition · category theory

DerivedCategory.TStructure.t

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : HasDerivedCategory C] → CategoryTheory.Triangulated.TStructure (DerivedCategory C)

The canonical t-structure on DerivedCategory C.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.TStructure
Cited by
13 results in Mathlib
Foundations
Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DerivedCategory.IsGE · cited by 8DerivedCategory.IsGEDerivedCategory.IsLE · cited by 7DerivedCategory.IsLEDerivedCategory.Plus · cited by 7DerivedCategory.PlusDerivedCategory.Plus.ι · cited by 6Plus.ιDerivedCategory.Plus.homologyFunctor · cited by 3Plus.homologyFunctorCochainComplex.Plus.modelCategoryQuillen.exists_quasiIso_injective · cited by 1modelCategoryQuillen.exis…DerivedCategory.isGE_iff · cited by 1DerivedCategory.isGE_iffDerivedCategory.isLE_iff · cited by 1DerivedCategory.isLE_iffDerivedCategory.Plus.Q · cited by 1Plus.QDerivedCategory.Plus.Qh · cited by 1Plus.QhDerivedCategory.Plus.isGE_ι_obj_iff · cited by 1Plus.isGE_ι_obj_iffDerivedCategory.exists_iso_Q_obj_of_isGE · cited by 1DerivedCategory.exists_is…DerivedCategory.exists_iso_Q_obj_of_isGE_of_isLE · cited by 1DerivedCategory.exists_is…DerivedCategory.exists_iso_Q_obj_of_isLE · cited by 1DerivedCategory.exists_is…CategoryTheory.Functor.rightDerivedFunctorPlus · cited by 0Functor.rightDerivedFunct…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCochainComplex · cited by 1016CochainComplexCategoryTheory.Triangulated.TStructure · cited by 318Triangulated.TStructureHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryDerivedCategory.Q · cited by 102DerivedCategory.QCochainComplex.IsStrictlyGE · cited by 34CochainComplex.IsStrictly…CochainComplex.IsStrictlyLE · cited by 20CochainComplex.IsStrictly…TStructure.tCITED BYCITES

Cites12

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

Cited by31

Results whose statement or proof uses this declaration.