Theorems · Theorem · category theory
CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE_trans
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} 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) (a b c : ℤ) (hab : a ≤ b) (hbc : b ≤ c),
CategoryTheory.CategoryStruct.comp (t.natTransTruncLEOfLE a b hab) (t.natTransTruncLEOfLE b c hbc) =
t.natTransTruncLEOfLE a c ⋯- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- LE.le.transstatement · cited by 3,151
- 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
- CategoryTheory.Pretriangulatedstatement and proof · cited by 669
- CategoryTheory.Triangulated.TStructurestatement and proof · cited by 318
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Triangulated.TStructure.natTransTruncLEOfLE_trans_appproof · cited by 1