Theorems · Definition · category theory
CochainComplex.HomComplex.Cochain.comp
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{F G K : CochainComplex C ℤ} →
{n₁ n₂ n₁₂ : ℤ} →
CochainComplex.HomComplex.Cochain F G n₁ →
CochainComplex.HomComplex.Cochain G K n₂ → n₁ + n₂ = n₁₂ → CochainComplex.HomComplex.Cochain F K n₁₂The composition of cochains.
- Cited by
- 115 results in Mathlib
- Foundations
- Depth 51 from the axioms, rests on 813 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cochainstatement and proof · cited by 341
- CochainComplex.HomComplex.Cochain.vproof · cited by 213
- CochainComplex.HomComplex.Cochain.mkproof · cited by 8
Cited by133
Results whose statement or proof uses this declaration.
- CochainComplex.HomComplex.Cochain.comp_vstatement and proof · cited by 30
- CochainComplex.mappingCone.descCochainproof · cited by 20
- CochainComplex.mappingCone.mapproof · cited by 19
- CochainComplex.mappingCone.liftCochainproof · cited by 18
- CochainComplex.HomComplex.Cochain.comp_zero_cochain_vstatement · cited by 17
- CochainComplex.HomComplex.Cochain.zero_cochain_comp_vstatement · cited by 17
- CochainComplex.mappingCone.liftstatement and proof · cited by 12
- CochainComplex.mappingCone.descCocyclestatement and proof · cited by 8
- CochainComplex.HomComplex.Cochain.comp_assoc_of_second_is_zero_cochainstatement · cited by 7
- CochainComplex.mappingCone.mapOfHomotopyproof · cited by 7
- CochainComplex.HomComplex.Cochain.zero_compstatement and proof · cited by 7
- CochainComplex.mappingCocone.descstatement and proof · cited by 6