Theorems · Definition · category theory
DerivedCategory.singleFunctor
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[inst_2 : HasDerivedCategory C] → ℤ → CategoryTheory.Functor C (DerivedCategory C)The single functor C ⥤ DerivedCategory C which sends X : C to the
single cochain complex with X sitting in degree n : ℤ.
- Cited by
- 78 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Functorstatement · cited by 16,252
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
- CategoryTheory.SingleFunctors.functorproof · cited by 64
- DerivedCategory.singleFunctorsproof · cited by 13
Cited by91
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.homstatement · cited by 42
- CategoryTheory.Abelian.Ext.extstatement · cited by 31
- CategoryTheory.Abelian.Ext.comp_homstatement · cited by 27
- CategoryTheory.ShortComplex.ShortExact.singleTriangleproof · cited by 26
- CategoryTheory.Abelian.Ext.mk₀_homstatement · cited by 20
- CategoryTheory.Functor.mapDerivedCategorySingleFunctorstatement · cited by 13
- CategoryTheory.ShortComplex.ShortExact.singleδstatement · cited by 12
- CategoryTheory.Abelian.Ext.mk₀_comp_mk₀proof · cited by 10
- CategoryTheory.Abelian.Ext.zero_compproof · cited by 10
- DerivedCategory.singleFunctorIsoCompQstatement and proof · cited by 10
- CategoryTheory.Abelian.Ext.homAddEquivstatement and proof · cited by 9
- CategoryTheory.Abelian.Ext.homEquivstatement · cited by 8