Theorems · Definition · category theory
CategoryTheory.Pretriangulated.contractibleTriangleFunctor
(C : Type u) →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.HasShift C ℤ] →
[CategoryTheory.Limits.HasZeroObject C] →
[CategoryTheory.Limits.HasZeroMorphisms C] →
CategoryTheory.Functor C (CategoryTheory.Pretriangulated.Triangle C)The functor C ⥤ Triangle C which sends X to contractibleTriangle X.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Homproof · cited by 32,603
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
- CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
- CategoryTheory.Pretriangulated.Trianglestatement · cited by 645
- CategoryTheory.Pretriangulated.contractibleTriangleproof · cited by 27
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₁statement and proof · cited by 0
- CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₂statement and proof · cited by 0
- CategoryTheory.Pretriangulated.contractibleTriangleFunctor_map_hom₃statement and proof · cited by 0
- CategoryTheory.Pretriangulated.contractibleTriangleFunctor_objstatement and proof · cited by 0
- CategoryTheory.Functor.contractible_mem_essImageDistTriangproof · cited by 0