Theorems · Definition · category theory
CategoryTheory.ShortComplex.ShortExact.singleTriangle.map
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Abelian C] →
[inst_2 : HasDerivedCategory C] →
{S₁ S₂ : CategoryTheory.ShortComplex C} →
(h₁ : S₁.ShortExact) → (h₂ : S₂.ShortExact) → (S₁ ⟶ S₂) → (h₁.singleTriangle ⟶ h₂.singleTriangle)The morphism h₁.singleTriangle h₁ ⟶ h₂.singleTriangle that is induced by a
map of short exact sequences of objects of C.
- Cited by
- 4 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.
Cites14
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.mapproof · cited by 8,698
- CategoryTheory.ShortComplexstatement and proof · cited by 1,850
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
- CategoryTheory.ShortComplex.Hom.τ₂proof · cited by 243
- CategoryTheory.ShortComplex.ShortExactstatement and proof · cited by 232
- CategoryTheory.ShortComplex.Hom.τ₃proof · cited by 197
- CategoryTheory.ShortComplex.Hom.τ₁proof · cited by 194
- HasDerivedCategorystatement and proof · cited by 190
- DerivedCategorystatement · cited by 165
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.singleTriangle.map_hom₁statement and proof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.singleTriangle.map_hom₃statement and proof · cited by 1
- CategoryTheory.ShortComplex.ShortExact.singleTriangle.map_hom₂statement and proof · cited by 0
- CategoryTheory.ShortComplex.ShortExact.extClass_naturalityproof · cited by 0