Theorems · Theorem · category theory
DerivedCategory.isIso_Qh_map_iff
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : HasDerivedCategory C] {X Y : HomotopyCategory C (ComplexShape.up ℤ)} (f : X ⟶ Y),
CategoryTheory.IsIso (DerivedCategory.Qh.map f) ↔ HomotopyCategory.quasiIso C (ComplexShape.up ℤ) f- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- ComplexShape.upstatement and proof · cited by 1,123
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
- HomotopyCategorystatement and proof · cited by 132
- CategoryTheory.Localization.invertsproof · cited by 63
- DerivedCategory.Qhstatement and proof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- DerivedCategory.isIso_iffproof · cited by 1
- DerivedCategory.left_facproof · cited by 1
- DerivedCategory.right_facproof · cited by 1