Theorems · Definition · category theory

DerivedCategory.Plus.homologyFunctor

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : HasDerivedCategory C] → ℤ → CategoryTheory.Functor (DerivedCategory.Plus C) C

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

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Plus
Cited by: 3 results in Mathlib
Foundations: Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian HasDerivedCategory

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites11

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.compproof · cited by 6,529
CategoryTheory.Abelianstatement and proof · cited by 1,753
HasDerivedCategorystatement and proof · cited by 190
DerivedCategorystatement · cited by 165
DerivedCategory.homologyFunctorproof · cited by 35
DerivedCategory.TStructure.tstatement · cited by 13
CategoryTheory.Triangulated.TStructure.plusstatement · cited by 7
DerivedCategory.Plusstatement · cited by 7
DerivedCategory.Plus.ιproof · cited by 6

Cited by3

Results whose statement or proof uses this declaration.

DerivedCategory.Plus.isZero_homology_of_isGEstatement · cited by 0
DerivedCategory.Plus.isZero_homology_of_isLEstatement · cited by 0
DerivedCategory.Plus.isIso_iffstatement and proof · cited by 0