Theorems · Theorem · category theory
CochainComplex.mappingCone.inl_v_fst_v
∀ {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 : q + 1 = p),
CategoryTheory.CategoryStruct.comp ((CochainComplex.mappingCone.inl φ).v p q ⋯)
((↑(CochainComplex.mappingCone.fst φ)).v q p hpq) =
CategoryTheory.CategoryStruct.id (F.X p)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- AddSubgroupstatement · cited by 3,232
- HomologicalComplex.Xstatement and proof · cited by 1,839
- 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.HomComplex.Cochain.vstatement · cited by 213
Cited by7
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.inl_v_fst_v_assocproof · cited by 6
- CochainComplex.mappingCone.lift_fproof · cited by 2
- CochainComplex.mappingCone.inl_fstproof · cited by 2
- CochainComplex.mappingCocone.inl_v_fst_fproof · cited by 1
- CochainComplex.mappingCone.decomp_toproof · cited by 1
- CochainComplex.mappingCone.triangleMapOfHomotopy_comm₃proof · cited by 1
- CochainComplex.mappingCone.map_inrproof · cited by 0