Theorems · Theorem · category theory
CochainComplex.mappingCone.inl_v_snd_v_assoc
∀ {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] (p q : ℤ) (hpq : p + -1 = q)
{Z : C} (h : G.X q ⟶ Z),
CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.inl φ).v p q hpq)
(CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.snd φ).v q q ⋯) h) =
CategoryTheory.CategoryStruct.comp 0 h- Cited by
- 5 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- add_zerostatement and proof · cited by 2,707
- HomologicalComplex.Xstatement and proof · cited by 1,839
- ComplexShape.upstatement · cited by 1,123
- CochainComplexstatement and proof · cited by 1,016
- HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
- CochainComplex.HomComplex.Cochain.vstatement and proof · cited by 213
- CochainComplex.mappingConestatement · cited by 181
Cited by5
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.mapHomologicalComplexIso_hom_descShortComplexproof · cited by 2
- CochainComplex.mappingCone.homologySequenceδ_trianglehproof · cited by 1
- CochainComplex.mappingCone.desc_fproof · cited by 1
- CochainComplex.mappingCone.decomp_fromproof · cited by 0