Theorems · Definition · category theory

CochainComplex.Plus.fibrantObjectEquivalence

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      CochainComplex.Plus (CategoryTheory.InjectiveObject C) ≌ HomotopicalAlgebra.FibrantObject (CochainComplex.Plus C)

The equivalence between CochainComplex.Plus (InjectiveObject C) and the category of fibrant object in CochainComplex.Plus C for the Quillen model category structure.

Defined in: Mathlib.Algebra.Homology.DerivedCategory.DerivabilityStructureInjectives
Cited by: 0 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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Cites20

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.compproof · cited by 6,529
CategoryTheory.Functor.idproof · cited by 3,333
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.Iso.reflproof · cited by 727
CategoryTheory.Equivalencestatement · cited by 601
CategoryTheory.ObjectProperty.liftproof · cited by 33
CochainComplex.plusstatement and proof · cited by 24
HomotopicalAlgebra.FibrantObjectstatement and proof · cited by 21
CochainComplex.Plusstatement and proof · cited by 20

Cited by1

Results whose statement or proof uses this declaration.

CochainComplex.Plus.fibrantObjectLocalizerMorphismproof · cited by 0