Theorems · Theorem · category theory
CochainComplex.HomComplex.Cochain.comp_assoc
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
{F G K L : CochainComplex C ℤ} {n₁ n₂ n₃ n₁₂ n₂₃ n₁₂₃ : ℤ} (z₁ : CochainComplex.HomComplex.Cochain F G n₁)
(z₂ : CochainComplex.HomComplex.Cochain G K n₂) (z₃ : CochainComplex.HomComplex.Cochain K L n₃) (h₁₂ : n₁ + n₂ = n₁₂)
(h₂₃ : n₂ + n₃ = n₂₃) (h₁₂₃ : n₁ + n₂ + n₃ = n₁₂₃), (z₁.comp z₂ h₁₂).comp z₃ ⋯ = z₁.comp (z₂.comp z₃ h₂₃) ⋯The associativity of the composition of cochains.
- Cited by
- 6 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.
Cites13
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.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplex.Xproof · cited by 1,839
- CochainComplexstatement and proof · cited by 1,016
- add_assocproof · cited by 746
- CochainComplex.HomComplex.Cochainstatement and proof · cited by 341
- CochainComplex.HomComplex.Cochain.vproof · cited by 213
- CochainComplex.HomComplex.Cochain.compstatement and proof · cited by 115
- CochainComplex.HomComplex.Cochain.extproof · cited by 68
Cited by6
Results whose statement or proof uses this declaration.
- CochainComplex.HomComplex.Cochain.comp_assoc_of_second_is_zero_cochainproof · cited by 7
- CochainComplex.mappingCone.inl_fst_assocproof · cited by 3
- CochainComplex.HomComplex.Cochain.comp_assoc_of_first_is_zero_cochainproof · cited by 3
- CochainComplex.HomComplex.Cochain.comp_assoc_of_third_is_zero_cochainproof · cited by 1
- CochainComplex.mappingCone.liftCochain_descCochainproof · cited by 1