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.QThe isomorphism singleFunctor C n ≅ CochainComplex.singleFunctor C n ⋙ Q.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Functor.compstatement · cited by 6,529
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement · cited by 1,016
- CategoryTheory.Iso.reflproof · cited by 727
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
- CochainComplex.singleFunctorstatement · cited by 111
- DerivedCategory.Qstatement · cited by 102
Cited by11
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.mapDerivedCategorySingleFunctorproof · cited by 13
- CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_mk_homstatement · cited by 3
- CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_mk_homstatement and proof · cited by 3
- CategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_addproof · cited by 1
- CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_addproof · cited by 1
- CategoryTheory.InjectiveResolution.extMk_homstatement · cited by 1
- CategoryTheory.ProjectiveResolution.extMk_homstatement · cited by 1
- CategoryTheory.InjectiveResolution.extMk_comp_mk₀proof · cited by 0
- CategoryTheory.ProjectiveResolution.extMk_comp_mk₀proof · cited by 0
- CategoryTheory.ProjectiveResolution.mk₀_comp_extMkproof · cited by 0
- CategoryTheory.InjectiveResolution.mk₀_comp_extMkproof · cited by 0