Theorems · Definition · category theory

DerivedCategory.singleFunctorsPostcompQIso

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

The isomorphism DerivedCategory.singleFunctors C ≅ (CochainComplex.singleFunctors C).postcomp Q.

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by: 9 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian HasDerivedCategory

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Around this declaration

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

Cites21

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.Isostatement · cited by 3,963
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement and proof · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.Iso.transproof · cited by 566
CategoryTheory.Functor.mapIsoproof · cited by 224
HasDerivedCategorystatement and proof · cited by 190
DerivedCategorystatement · cited by 165
HomotopyCategory.quotientproof · cited by 109
DerivedCategory.Qstatement · cited by 102
CategoryTheory.SingleFunctorsstatement · cited by 65

Cited by12

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.ShortExact.singleδproof · cited by 12
CategoryTheory.ShortComplex.ShortExact.singleTriangleIsoproof · cited by 7
CategoryTheory.ShortComplex.ShortExact.extClass_homproof · cited by 6
DerivedCategory.singleFunctorsPostcompQIso_hom_homstatement · cited by 2
DerivedCategory.singleFunctorsPostcompQIso_inv_homstatement · cited by 2
DerivedCategory.singleFunctorCompHomologyFunctorIsoproof · cited by 0
CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁statement · cited by 0
CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃statement · cited by 0
CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂statement · cited by 0
CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁statement · cited by 0
CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₂statement · cited by 0
CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₃statement · cited by 0