Theorems · Definition · category theory
CochainComplex.mappingCone.inl
{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] →
CochainComplex.HomComplex.Cochain F (CochainComplex.mappingCone φ) (-1)The left inclusion in the mapping cone, as a cochain of degree -1.
- Cited by
- 61 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CochainComplex.HomComplex.Cochainstatement · cited by 341
- HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
- CochainComplex.mappingConestatement · cited by 181
- HomologicalComplex.homotopyCofiber.inlXproof · cited by 29
- CochainComplex.HomComplex.Cochain.mkproof · cited by 8
Cited by75
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.mapproof · cited by 19
- CochainComplex.mappingCone.liftCochainproof · cited by 18
- CochainComplex.mappingCocone.inlproof · cited by 11
- CochainComplex.mappingCone.ext_from_iffstatement and proof · cited by 9
- CochainComplex.mappingCone.inl_v_fst_vstatement · cited by 7
- CochainComplex.mappingCone.mapOfHomotopyproof · cited by 7
- CochainComplex.mappingCone.inl_v_fst_v_assocstatement and proof · cited by 6
- CochainComplex.mappingCone.inl_v_snd_vstatement · cited by 6
- CochainComplex.mappingCone.inl_v_desc_fstatement and proof · cited by 5
- CochainComplex.mappingCone.inl_v_desc_f_assocstatement and proof · cited by 5
- CochainComplex.mappingCone.inl_v_snd_v_assocstatement and proof · cited by 5
- CochainComplex.mappingCone.inl_v_triangle_mor₃_fstatement and proof · cited by 5