Theorems · Definition · category theory
DerivedCategory.singleFunctors
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[inst_2 : HasDerivedCategory C] → CategoryTheory.SingleFunctors C (DerivedCategory C) ℤThe single functors C ⥤ DerivedCategory C for all n : ℤ along with
their compatibilities with shifts.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Abelianstatement and proof · cited by 1,753
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
- CategoryTheory.SingleFunctorsstatement · cited by 65
- DerivedCategory.Qhproof · cited by 27
- CategoryTheory.SingleFunctors.postcompproof · cited by 22
- HomotopyCategory.singleFunctorsproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- DerivedCategory.singleFunctorproof · cited by 78
- DerivedCategory.singleFunctorsPostcompQIsostatement · cited by 9
- CategoryTheory.ShortComplex.ShortExact.singleTriangleIsoproof · cited by 7
- CategoryTheory.ShortComplex.ShortExact.extClass_homproof · cited by 6
- CategoryTheory.Abelian.Ext.eq_zero_of_projectiveproof · cited by 4
- CategoryTheory.Abelian.Ext.eq_zero_of_injectiveproof · cited by 4
- DerivedCategory.singleFunctorsPostcompQIso_hom_homstatement and proof · cited by 2
- DerivedCategory.singleFunctorsPostcompQIso_inv_homstatement · cited by 2
- CategoryTheory.ShortComplex.ShortExact.mapShiftedHom_singleδ'proof · cited by 2
- CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGEproof · cited by 0
- CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁statement · cited by 0
- DerivedCategory.singleFunctorsPostcompQhIsostatement and proof · cited by 0