Theorems · Theorem · category theory
CochainComplex.HomComplex.Cochain.comp_assoc_of_second_is_zero_cochain
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
{F G K L : CochainComplex C ℤ} {n₁ n₃ n₁₃ : ℤ} (z₁ : CochainComplex.HomComplex.Cochain F G n₁)
(z₂ : CochainComplex.HomComplex.Cochain G K 0) (z₃ : CochainComplex.HomComplex.Cochain K L n₃) (h₁₃ : n₁ + n₃ = n₁₃),
(z₁.comp z₂ ⋯).comp z₃ h₁₃ = z₁.comp (z₂.comp z₃ ⋯) h₁₃- Cited by
- 7 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- add_zerostatement and proof · cited by 2,707
- zero_addstatement and proof · cited by 2,366
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cochainstatement and proof · cited by 341
- CochainComplex.HomComplex.Cochain.compstatement · cited by 115
- CochainComplex.HomComplex.Cochain.comp_assocproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.inl_snd_assocproof · cited by 3
- CochainComplex.mappingCone.liftCochain_sndproof · cited by 2
- CochainComplex.mappingCone.liftCochain_fstproof · cited by 2
- CochainComplex.mappingCone.δ_descCochainproof · cited by 1
- CochainComplex.mappingCone.δ_liftCochainproof · cited by 1
- CochainComplex.mappingCone.liftCochain_descCochainproof · cited by 1
- CochainComplex.mappingCocone.δ_liftCochainproof · cited by 0