Theorems · Definition · category theory

CochainComplex.Plus.fibrantObjectLocalizerMorphism

(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)
        (HomotopicalAlgebra.weakEquivalences (HomotopicalAlgebra.FibrantObject (CochainComplex.Plus C)))

The localizer morphism (relative to quasi-isomorphisms) that is given by the equivalence of categories CochainComplex.Plus (InjectiveObject C) ≌ FibrantObject (CochainComplex.Plus C).

Defined in: Mathlib.Algebra.Homology.DerivedCategory.DerivabilityStructureInjectives
Cited by: 0 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Equivalence.functorproof · cited by 1,268
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.LocalizerMorphismstatement · cited by 161
CategoryTheory.MorphismProperty.inverseImagestatement · cited by 83
HomotopicalAlgebra.weakEquivalencesstatement · cited by 44
CochainComplex.plusstatement · cited by 24
HomotopicalAlgebra.FibrantObjectstatement · cited by 21
CochainComplex.Plusstatement · cited by 20
HomotopicalAlgebra.fibrantObjectsstatement · cited by 20

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