Theorems · Definition · category theory
CochainComplex.mappingCone.inr
{C : Type u_1} →
[inst : CategoryTheory.Category.{v, u_1} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{F G : CochainComplex C ℤ} →
(φ : F ⟶ G) → [inst_2 : HomologicalComplex.HasHomotopyCofiber φ] → G ⟶ CochainComplex.mappingCone φThe right inclusion in the mapping cone.
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 40 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.Homstatement and proof · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
- CochainComplex.mappingConestatement · cited by 181
- HomologicalComplex.homotopyCofiber.inrproof · cited by 17
Cited by94
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.triangleproof · cited by 48
- CochainComplex.mappingConeCompTriangleproof · cited by 20
- CochainComplex.mappingCone.mapproof · cited by 19
- CochainComplex.mappingCone.liftCochainproof · cited by 18
- CochainComplex.mappingCocone.inrproof · cited by 11
- CochainComplex.mappingCone.ext_from_iffstatement and proof · cited by 9
- CochainComplex.mappingCone.inr_f_fst_vstatement · cited by 9
- CochainComplex.mappingCone.inr_f_desc_fstatement and proof · cited by 8
- CochainComplex.mappingCone.inr_f_snd_vstatement · cited by 7
- CochainComplex.mappingCone.mapOfHomotopyproof · cited by 7
- CochainComplex.mappingCone.inr_f_triangle_mor₃_fstatement and proof · cited by 6
- CochainComplex.mappingCone.inr_descstatement and proof · cited by 4