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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) C

The homology functor DerivedCategory C ⥤ C in degree n : ℤ.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.HomologySequence
Cited by
35 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianHasDerivedCategory

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

DerivedCategory.homologyFunctorFactors · cited by 20DerivedCategory.homologyF…DerivedCategory.HomologySequence.δ · cited by 15HomologySequence.δDerivedCategory.homologyFunctorFactorsh · cited by 9DerivedCategory.homologyF…DerivedCategory.homologyFunctorFactors_hom_naturality · cited by 6DerivedCategory.homologyF…CochainComplex.homologyFunctorFactors_hom_app_homologyδOfTriangle · cited by 4CochainComplex.homologyFu…DerivedCategory.HomologySequence.comp_δ · cited by 3HomologySequence.comp_δDerivedCategory.HomologySequence.δ_comp · cited by 3HomologySequence.δ_compDerivedCategory.Plus.homologyFunctor · cited by 3Plus.homologyFunctorDerivedCategory.homologyFunctorFactorsh_hom_app_quotient_obj · cited by 2DerivedCategory.homologyF…DerivedCategory.homologyFunctorFactorsh_inv_app_quotient_obj · cited by 2DerivedCategory.homologyF…CochainComplex.homologyMap_comp_eq_zero_of_distTriang · cited by 2CochainComplex.homologyMa…DerivedCategory.isGE_Q_obj_iff · cited by 2DerivedCategory.isGE_Q_ob…DerivedCategory.shiftMap_homologyFunctor_map_Q · cited by 2DerivedCategory.shiftMap_…DerivedCategory.shiftMap_homologyFunctor_map_Qh · cited by 2DerivedCategory.shiftMap_…CochainComplex.homologyMap_homologyδOfTriangle · cited by 2CochainComplex.homologyMa…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianComplexShape.up · cited by 1123ComplexShape.upHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryHomologicalComplexUpToQuasiIso.homologyFunctor · cited by 4HomologicalComplexUpToQua…DerivedCategory.homologyFunct…CITED BYCITES

Cites7

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Cited by40

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