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Theorems · Definition · category theory

DerivedCategory.singleFunctors

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] →
      [inst_2 : HasDerivedCategory C] → CategoryTheory.SingleFunctors C (DerivedCategory C) ℤ

The single functors C ⥤ DerivedCategory C for all n : ℤ along with their compatibilities with shifts.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by
13 results in Mathlib
Foundations
Depth 104 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.

DerivedCategory.singleFunctor · cited by 78DerivedCategory.singleFun…DerivedCategory.singleFunctorsPostcompQIso · cited by 9DerivedCategory.singleFun…CategoryTheory.ShortComplex.ShortExact.singleTriangleIso · cited by 7ShortExact.singleTriangle…CategoryTheory.ShortComplex.ShortExact.extClass_hom · cited by 6ShortExact.extClass_homCategoryTheory.Abelian.Ext.eq_zero_of_projective · cited by 4Ext.eq_zero_of_projectiveCategoryTheory.Abelian.Ext.eq_zero_of_injective · cited by 4Ext.eq_zero_of_injectiveDerivedCategory.singleFunctorsPostcompQIso_hom_hom · cited by 2DerivedCategory.singleFun…DerivedCategory.singleFunctorsPostcompQIso_inv_hom · cited by 2DerivedCategory.singleFun…CategoryTheory.ShortComplex.ShortExact.mapShiftedHom_singleδ' · cited by 2ShortExact.mapShiftedHom_…CategoryTheory.HasExt.hasSmallLocalizedShiftedHom_of_isLE_of_isGE · cited by 0HasExt.hasSmallLocalizedS…CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₁ · cited by 0ShortExact.singleTriangle…DerivedCategory.singleFunctorsPostcompQhIso · cited by 0DerivedCategory.singleFun…CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₂ · cited by 0ShortExact.singleTriangle…CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_hom_hom₃ · cited by 0ShortExact.singleTriangle…CategoryTheory.ShortComplex.ShortExact.singleTriangleIso_inv_hom₁ · cited by 0ShortExact.singleTriangle…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryCategoryTheory.SingleFunctors · cited by 65CategoryTheory.SingleFunc…DerivedCategory.Qh · cited by 27DerivedCategory.QhCategoryTheory.SingleFunctors.postcomp · cited by 22SingleFunctors.postcompHomotopyCategory.singleFunctors · cited by 3HomotopyCategory.singleFu…DerivedCategory.singleFunctorsCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.