Theorems · Theorem · category theory

HomotopyCategory.Plus.isIso_quotient_map_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  {K L : CochainComplex.Plus (CategoryTheory.InjectiveObject C)} (f : K ⟶ L),
  CategoryTheory.IsIso ((HomotopyCategory.Plus.quotient (CategoryTheory.InjectiveObject C)).map f) ↔
    CochainComplex.Plus.quasiIso C ((CategoryTheory.InjectiveObject.ι C).mapCochainComplexPlus.map f)

Defined in: Mathlib.Algebra.Homology.DerivedCategory.DerivabilityStructureInjectives
Cited by: 0 results in Mathlib
Foundations: Depth 104 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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functor.mapstatement and proof · cited by 8,698
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.IsIsostatement · cited by 1,156
ComplexShape.upstatement and proof · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.InducedCategory.Hom.homproof · cited by 850
CategoryTheory.Functor.mapHomologicalComplexproof · cited by 145
HomotopyCategorystatement · cited by 132
CochainComplex.plusstatement · cited by 24

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