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Theorems · Definition · category theory

DerivedCategory.singleFunctorIsoCompQ

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : HasDerivedCategory C] →
        (n : ℤ) → DerivedCategory.singleFunctor C n ≅ (CochainComplex.singleFunctor C n).comp DerivedCategory.Q

The isomorphism singleFunctor C n ≅ CochainComplex.singleFunctor C n ⋙ Q.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by
10 results in Mathlib
Foundations
Depth 106 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.

CategoryTheory.Functor.mapDerivedCategorySingleFunctor · cited by 13Functor.mapDerivedCategor…CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_hom · cited by 3InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_hom · cited by 3ProjectiveResolution.extE…CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add · cited by 1InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add · cited by 1ProjectiveResolution.extE…CategoryTheory.InjectiveResolution.extMk_hom · cited by 1InjectiveResolution.extMk…CategoryTheory.ProjectiveResolution.extMk_hom · cited by 1ProjectiveResolution.extM…CategoryTheory.InjectiveResolution.extMk_comp_mk₀ · cited by 0InjectiveResolution.extMk…CategoryTheory.ProjectiveResolution.extMk_comp_mk₀ · cited by 0ProjectiveResolution.extM…CategoryTheory.ProjectiveResolution.mk₀_comp_extMk · cited by 0ProjectiveResolution.mk₀_…CategoryTheory.InjectiveResolution.mk₀_comp_extMk · cited by 0InjectiveResolution.mk₀_c…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianComplexShape.up · cited by 1123ComplexShape.upCochainComplex · cited by 1016CochainComplexCategoryTheory.Iso.refl · cited by 727Iso.reflHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryCochainComplex.singleFunctor · cited by 111CochainComplex.singleFunc…DerivedCategory.Q · cited by 102DerivedCategory.QDerivedCategory.singleFunctor · cited by 78DerivedCategory.singleFun…DerivedCategory.singleFunctor…CITED BYCITES

Cites13

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Cited by11

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