Theorems · Definition · category theory
CochainComplex.mappingCone
{C : Type u_1} →
[inst : CategoryTheory.Category.{v, u_1} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{F G : CochainComplex C ℤ} → (φ : F ⟶ G) → [HomologicalComplex.HasHomotopyCofiber φ] → CochainComplex C ℤThe mapping cone of a morphism of cochain complexes indexed by ℤ.
- Cited by
- 181 results in Mathlib
- Foundations
- Depth 38 from the axioms, rests on 687 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- HomologicalComplex.homotopyCofiberproof · cited by 31
Cited by218
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.inrstatement · cited by 79
- CochainComplex.mappingCone.inlstatement · cited by 61
- CochainComplex.mappingCone.fststatement · cited by 51
- CochainComplex.mappingCone.sndstatement · cited by 49
- CochainComplex.mappingCoconeproof · cited by 46
- CategoryTheory.ShortComplex.ShortExact.extClassproof · cited by 36
- CochainComplex.mappingCone.descCochainstatement · cited by 20
- CochainComplex.mappingCone.descstatement · cited by 19
- CochainComplex.mappingCone.mapstatement · cited by 19
- CochainComplex.mappingCone.descShortComplexstatement · cited by 18
- CochainComplex.mappingCone.liftCochainstatement · cited by 18
- CochainComplex.mappingCone.liftstatement · cited by 12
Showing the 200 most cited of 218.