Theorems · Definition · category theory
CochainComplex.HomComplex.cocycle
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] →
(F G : CochainComplex C ℤ) → (n : ℤ) → AddSubgroup (CochainComplex.HomComplex.Cochain F G n)The subgroup of cocycles in Cochain F G n.
- Cited by
- 105 results in Mathlib
- Foundations
- Depth 53 from the axioms, rests on 1,106 definitions · 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
- AddSubgroupstatement · cited by 3,232
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cochainstatement · cited by 341
- AddMonoidHom.kerproof · cited by 158
- LinearMap.toAddMonoidHomproof · cited by 101
- CochainComplex.HomComplex.δ_homproof · cited by 6
Cited by113
Results whose statement or proof uses this declaration.
- CochainComplex.HomComplex.Cocycleproof · cited by 130
- CochainComplex.HomComplex.Cocycle.extstatement · cited by 19
- CochainComplex.HomComplex.Cocycle.ofHom_coestatement · cited by 19
- CochainComplex.HomComplex.Cocycle.homOf_fstatement · cited by 13
- CochainComplex.mappingCone.liftstatement · cited by 12
- CochainComplex.mappingCone.inr_f_fst_vstatement · cited by 9
- CochainComplex.mappingCone.descCocyclestatement · cited by 8
- CochainComplex.mappingCone.inl_v_fst_vstatement · cited by 7
- CochainComplex.HomComplex.Cocycle.fromSingleMk_coestatement · cited by 7
- CochainComplex.HomComplex.Cocycle.toSingleMk_coestatement · cited by 7
- CochainComplex.mappingCocone.descstatement · cited by 6
- CochainComplex.mappingCone.descCocycle_coestatement · cited by 6