Theorems · Definition · category theory
DerivedCategory.homologyFunctor
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[inst_2 : HasDerivedCategory C] → ℤ → CategoryTheory.Functor (DerivedCategory C) CThe homology functor DerivedCategory C ⥤ C in degree n : ℤ.
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 99 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
- ComplexShape.upproof · cited by 1,123
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
- HomologicalComplexUpToQuasiIso.homologyFunctorproof · cited by 4
Cited by40
Results whose statement or proof uses this declaration.
- DerivedCategory.homologyFunctorFactorsstatement · cited by 20
- DerivedCategory.HomologySequence.δstatement and proof · cited by 15
- DerivedCategory.homologyFunctorFactorshstatement · cited by 9
- DerivedCategory.homologyFunctorFactors_hom_naturalitystatement · cited by 6
- CochainComplex.homologyFunctorFactors_hom_app_homologyδOfTrianglestatement and proof · cited by 4
- DerivedCategory.HomologySequence.comp_δstatement and proof · cited by 3
- DerivedCategory.HomologySequence.δ_compstatement and proof · cited by 3
- DerivedCategory.Plus.homologyFunctorproof · cited by 3
- DerivedCategory.homologyFunctorFactorsh_hom_app_quotient_objstatement · cited by 2
- DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_objstatement · cited by 2
- CochainComplex.homologyMap_comp_eq_zero_of_distTriangproof · cited by 2
- DerivedCategory.isGE_Q_obj_iffproof · cited by 2