Theorems · Theorem · category theory

DerivedCategory.singleFunctorsPostcompQIso_hom_hom

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : HasDerivedCategory C] (n : ℤ),
  (DerivedCategory.singleFunctorsPostcompQIso C).hom.hom n =
    CategoryTheory.CategoryStruct.id ((DerivedCategory.singleFunctors C).functor n)

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian HasDerivedCategory

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Cites27

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
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Iso.homstatement · cited by 7,684
CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.Abelianstatement and proof · cited by 1,753
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.Functor.map_idproof · cited by 616

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.ShortComplex.ShortExact.extClass_homproof · cited by 6
CategoryTheory.ShortComplex.ShortExact.mapShiftedHom_singleδ'proof · cited by 2