Theorems · Definition · category theory
CategoryTheory.ShortComplex.ShortExact.singleTriangle
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[inst_2 : HasDerivedCategory C] →
{S : CategoryTheory.ShortComplex C} → S.ShortExact → CategoryTheory.Pretriangulated.Triangle (DerivedCategory C)The (distinguished) triangle in the derived category of C given by a
short exact short complex in C.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.ShortComplex.gproof · cited by 658
- CategoryTheory.ShortComplex.fproof · cited by 653
- CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
- HasDerivedCategorystatement and proof · cited by 190
- CategoryTheory.Pretriangulated.Triangle.mkproof · cited by 183
- DerivedCategorystatement · cited by 165
- DerivedCategory.singleFunctorproof · cited by 78
Cited by28
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.singleTriangle_distinguishedstatement and proof · cited by 8
- CategoryTheory.ShortComplex.ShortExact.singleTriangleIsostatement and proof · cited by 7
- CategoryTheory.ShortComplex.ShortExact.singleTriangle.mapstatement · cited by 4
- 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.preadditiveCoyoneda_homologySequenceδ_singleTriangle_applystatement and proof · cited by 2
- CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_applystatement and proof · cited by 2
- 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.comp_extClassproof · cited by 1