Theorems · Definition · category theory
CochainComplex.mappingCocone.inr
{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) →
[inst_2 : HomologicalComplex.HasHomotopyCofiber φ] →
CochainComplex.HomComplex.Cocycle L (CochainComplex.mappingCocone φ) 1The right inclusion in Cocycle L (mappingCocone φ) 1.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.HomComplex.Cocyclestatement · cited by 130
- CochainComplex.mappingCone.inrproof · cited by 79
- CochainComplex.mappingCoconestatement · cited by 46
- CochainComplex.HomComplex.Cocycle.ofHomproof · cited by 23
- CochainComplex.HomComplex.Cocycle.rightShiftproof · cited by 7
Cited by11
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCocone.inr_v_descCochain_vstatement · cited by 3
- CochainComplex.mappingCocone.inr_v_desc_fstatement and proof · cited by 1
- CochainComplex.mappingCocone.inr_v_fst_fstatement and proof · cited by 1
- CochainComplex.mappingCocone.inr_v_snd_vstatement and proof · cited by 1
- CochainComplex.mappingCocone.id_Xstatement and proof · cited by 0
- CochainComplex.mappingCocone.inr_comp_descCochainstatement and proof · cited by 0
- CochainComplex.mappingCocone.inr_v_descCochain_v_assocstatement and proof · cited by 0
- CochainComplex.mappingCocone.inr_v_desc_f_assocstatement and proof · cited by 0
- CochainComplex.mappingCocone.inr_v_fst_f_assocstatement and proof · cited by 0
- CochainComplex.mappingCocone.inr_v_snd_v_assocstatement and proof · cited by 0
- CochainComplex.mappingCocone.δ_liftCochainstatement · cited by 0