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Theorems · Definition · category theory

DerivedCategory.singleFunctor

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

The single functor C ⥤ DerivedCategory C which sends X : C to the single cochain complex with X sitting in degree n : ℤ.

Defined in
Mathlib.Algebra.Homology.DerivedCategory.Basic
Cited by
78 results in Mathlib
Foundations
Depth 105 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.

CategoryTheory.Abelian.Ext.hom · cited by 42Ext.homCategoryTheory.Abelian.Ext.ext · cited by 31Ext.extCategoryTheory.Abelian.Ext.comp_hom · cited by 27Ext.comp_homCategoryTheory.ShortComplex.ShortExact.singleTriangle · cited by 26ShortExact.singleTriangleCategoryTheory.Abelian.Ext.mk₀_hom · cited by 20Ext.mk₀_homCategoryTheory.Functor.mapDerivedCategorySingleFunctor · cited by 13Functor.mapDerivedCategor…CategoryTheory.ShortComplex.ShortExact.singleδ · cited by 12ShortExact.singleδCategoryTheory.Abelian.Ext.mk₀_comp_mk₀ · cited by 10Ext.mk₀_comp_mk₀CategoryTheory.Abelian.Ext.zero_comp · cited by 10Ext.zero_compDerivedCategory.singleFunctorIsoCompQ · cited by 10DerivedCategory.singleFun…CategoryTheory.Abelian.Ext.homAddEquiv · cited by 9Ext.homAddEquivCategoryTheory.Abelian.Ext.homEquiv · cited by 8Ext.homEquivCategoryTheory.Abelian.Ext.mk₀_zero · cited by 7Ext.mk₀_zeroCategoryTheory.Abelian.Ext.comp_zero · cited by 7Ext.comp_zeroCategoryTheory.Abelian.Ext.zero_hom · cited by 6Ext.zero_homCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryCategoryTheory.SingleFunctors.functor · cited by 64SingleFunctors.functorDerivedCategory.singleFunctors · cited by 13DerivedCategory.singleFun…DerivedCategory.singleFunctorCITED BYCITES

Cites7

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Cited by91

Results whose statement or proof uses this declaration.