Theorems · Theorem · category theory
CategoryTheory.Triangulated.AbelianSubcategory.eq_zero_of_hom_shift_pos
∀ {C : Type u_1} {A : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.HasShift C ℤ] [∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive]
[inst_4 : CategoryTheory.Category.{v_2, u_2} A] {ι : CategoryTheory.Functor A C},
(∀ ⦃X Y : A⦄ ⦃n : ℤ⦄ (f : ι.obj X ⟶ (CategoryTheory.shiftFunctor C n).obj (ι.obj Y)), n < 0 → f = 0) →
∀ {X Y : A} {n : ℤ} (f : (CategoryTheory.shiftFunctor C n).obj (ι.obj X) ⟶ ι.obj Y), 0 < n → f = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.idproof · cited by 3,333
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Triangulated.AbelianSubcategory.mono_ιKproof · cited by 0
- CategoryTheory.Triangulated.AbelianSubcategory.epi_πQproof · cited by 0
- CategoryTheory.Triangulated.AbelianSubcategory.exists_desc_πQproof · cited by 0
- CategoryTheory.Triangulated.AbelianSubcategory.exists_lift_ιKproof · cited by 0