Theorems · Definition · category theory
CochainComplex.mappingCocone
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{K L : CochainComplex C ℤ} → (φ : K ⟶ L) → [HomologicalComplex.HasHomotopyCofiber φ] → CochainComplex C ℤThe mapping cocone of a morphism φ : K ⟶ L of cochain complexes: it is
(mappingCone φ)⟦(-1 : ℤ)⟧.
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.objproof · cited by 19,642
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.shiftFunctorproof · cited by 1,553
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
- CochainComplex.mappingConeproof · cited by 181
Cited by56
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCocone.fststatement · cited by 14
- CochainComplex.mappingCocone.descCochainstatement · cited by 12
- CochainComplex.mappingCocone.liftCochainstatement · cited by 12
- CochainComplex.mappingCocone.inlstatement · cited by 11
- CochainComplex.mappingCocone.inrstatement · cited by 11
- CochainComplex.mappingCocone.sndstatement · cited by 11
- CochainComplex.mappingCocone.liftstatement · cited by 8
- CochainComplex.mappingCocone.descstatement · cited by 6
- CochainComplex.mappingCocone.descCocyclestatement · cited by 5
- CochainComplex.mappingCocone.liftCocyclestatement · cited by 5
- CochainComplex.mappingCocone.descCocycle_coestatement · cited by 3
- CochainComplex.mappingCocone.inl_v_descCochain_vstatement · cited by 3