Theorems · Theorem · category theory
CategoryTheory.Triangulated.TStructure.from_truncGE_obj_ext
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
[inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.HasShift C ℤ]
[inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
(t : CategoryTheory.Triangulated.TStructure C) {n : ℤ} {X Y : C} {f₁ f₂ : (t.truncGE n).obj X ⟶ Y},
CategoryTheory.CategoryStruct.comp ((t.truncGEπ n).app X) f₁ =
CategoryTheory.CategoryStruct.comp ((t.truncGEπ n).app X) f₂ →
∀ [t.IsGE Y n], f₁ = f₂- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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.compstatement and proof · cited by 17,999
- CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
- CategoryTheory.Functor.idstatement · 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
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Functor.Additivestatement and proof · cited by 1,179
- sub_selfproof · cited by 996
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Triangulated.TStructure.isIso_truncGE_map_iffproof · cited by 2
- CategoryTheory.Triangulated.TStructure.truncGE_map_truncGEπ_appproof · cited by 2
- CategoryTheory.Triangulated.TStructure.isLE_iff_orthogonalproof · cited by 1