Theorems · Theorem · category theory

DerivedCategory.isZero_of_isGE

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : HasDerivedCategory C] (X : DerivedCategory C) (n i : ℤ),
  i < n → ∀ [hX : X.IsGE n], CategoryTheory.Limits.IsZero ((DerivedCategory.homologyFunctor C i).obj X)

Defined in: Mathlib.Algebra.Homology.DerivedCategory.TStructure
Cited by: 1 results in Mathlib
Foundations: Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian HasDerivedCategory DerivedCategory.IsGE

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Cites9

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

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Limits.IsZerostatement · cited by 306
HasDerivedCategorystatement and proof · cited by 190
DerivedCategorystatement and proof · cited by 165
DerivedCategory.homologyFunctorstatement · cited by 35
DerivedCategory.IsGEstatement and proof · cited by 8
DerivedCategory.isGE_iffproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

DerivedCategory.Plus.isZero_homology_of_isGEproof · cited by 0