Theorems · Theorem · category theory

DerivedCategory.from_singleFunctor_obj_eq_zero_of_projective

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : HasDerivedCategory C] {P : C} [CategoryTheory.Projective P] {L : CochainComplex C ℤ} {i : ℤ}
  (φ : DerivedCategory.Q.obj ((CochainComplex.singleFunctor C i).obj P) ⟶ DerivedCategory.Q.obj L),
  ∀ n < i, ∀ [L.IsStrictlyLE n], φ = 0

Defined in: Mathlib.Algebra.Homology.DerivedCategory.Ext.EnoughProjectives
Cited by: 1 results in Mathlib
Foundations: Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian HasDerivedCategory CategoryTheory.Projective CochainComplex.IsStrictlyLE

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites31

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.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.Functor.mapproof · cited by 8,698
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.IsIsoproof · cited by 1,156
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement and proof · cited by 1,016
HomologicalComplex.Hom.fproof · cited by 845
CategoryTheory.Functor.map_compproof · cited by 734

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Abelian.Ext.eq_zero_of_projectiveproof · cited by 4