Theorems · Theorem · category theory

CochainComplex.Plus.exists_quasiIso_injective

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  [CategoryTheory.EnoughInjectives C] (K : CochainComplex.Plus C) (n : ℤ) [K.obj.IsStrictlyGE n],
  ∃ L, ∃ (_ : L.obj.IsStrictlyGE n), ∃ i, CochainComplex.Plus.quasiIso C i

Defined in: Mathlib.Algebra.Homology.DerivedCategory.DerivabilityStructureInjectives
Cited by: 1 results in Mathlib
Foundations: Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.EnoughInjectives CochainComplex.IsStrictlyGE

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Cites23

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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
HomologicalComplex.Xproof · cited by 1,839
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
CategoryTheory.ObjectProperty.homMkproof · cited by 71
CategoryTheory.Injectiveproof · cited by 70
QuasiIsoproof · cited by 52
CategoryTheory.EnoughInjectivesstatement and proof · cited by 35

Cited by1

Results whose statement or proof uses this declaration.

DerivedCategory.Plus.exists_injective_nonempty_isoproof · cited by 0