Theorems · Definition · category theory

CochainComplex.Plus.localizerMorphism

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      CategoryTheory.LocalizerMorphism
        ((CochainComplex.Plus.quasiIso C).inverseImage (CategoryTheory.InjectiveObject.ι C).mapCochainComplexPlus)
        (CochainComplex.Plus.quasiIso C)

The localizer morphism (relative to quasi-isomorphisms) that is given by the "inclusion functor" CochainComplex.Plus (InjectiveObject C) ⥤ CochainComplex.Plus C.

Defined in: Mathlib.Algebra.Homology.DerivedCategory.DerivabilityStructureInjectives
Cited by: 1 results in Mathlib
Foundations: Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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Cites13

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.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.LocalizerMorphismstatement · cited by 161
CategoryTheory.MorphismProperty.inverseImagestatement · cited by 83
CochainComplex.plusstatement · cited by 24
CochainComplex.Plusstatement · cited by 20
CategoryTheory.Functor.mapCochainComplexPlusstatement and proof · cited by 11
CategoryTheory.InjectiveObjectstatement · cited by 6
CochainComplex.Plus.quasiIsostatement · cited by 6
CategoryTheory.isInjectivestatement · cited by 6

Cited by1

Results whose statement or proof uses this declaration.

CochainComplex.Plus.localizerMorphism_functorstatement and proof · cited by 0