Theorems · Theorem · category theory
CategoryTheory.ShortComplex.ShortExact.singleTriangle_distinguished
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : HasDerivedCategory C] {S : CategoryTheory.ShortComplex C} (hS : S.ShortExact),
hS.singleTriangle ∈ CategoryTheory.Pretriangulated.distinguishedTrianglesThe distinguished triangle in the derived category of C given by a
short exact short complex in C.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- ComplexShape.upproof · cited by 1,123
- CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
- CategoryTheory.Pretriangulated.distinguishedTrianglesstatement · cited by 316
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
- HomologicalComplex.singleproof · cited by 110
- CategoryTheory.Pretriangulated.isomorphic_distinguishedproof · cited by 47
Cited by8
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.contravariant_sequence_exact₁'proof · cited by 4
- CategoryTheory.Abelian.Ext.covariant_sequence_exact₃'proof · cited by 4
- CategoryTheory.Abelian.Ext.covariant_sequence_exact₁'proof · cited by 3
- CategoryTheory.Abelian.Ext.contravariant_sequence_exact₂'proof · cited by 2
- CategoryTheory.Abelian.Ext.contravariant_sequence_exact₃'proof · cited by 2
- CategoryTheory.Abelian.Ext.covariant_sequence_exact₂'proof · cited by 2
- CategoryTheory.ShortComplex.ShortExact.extClass_compproof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.comp_extClassproof · cited by 1