Theorems · Theorem · category theory
DerivedCategory.exists_iso_singleFunctor_obj_of_isGE_of_isLE
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : HasDerivedCategory C] (X : DerivedCategory C) (n : ℤ) [X.IsGE n] [X.IsLE n],
∃ Y, Nonempty (X ≅ (DerivedCategory.singleFunctor C n).obj Y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.objstatement and proof · cited by 19,642
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upproof · cited by 1,123
- CochainComplexproof · cited by 1,016
- CategoryTheory.Iso.transproof · cited by 566
- CategoryTheory.Functor.mapIsoproof · cited by 224
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement and proof · cited by 165
- HomologicalComplex.singleproof · cited by 110
- DerivedCategory.Qproof · cited by 102
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGEproof · cited by 0