Theorems · Definition · category theory
CochainComplex.HomComplex.Cocycle
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[inst_1 : CategoryTheory.Preadditive C] → CochainComplex C ℤ → CochainComplex C ℤ → ℤ → Type vThe type of n-cocycles, as a subtype of Cochain F G n.
- Cited by
- 130 results in Mathlib
- Foundations
- Depth 54 from the axioms, rests on 1,110 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- CochainComplexstatement and proof · cited by 1,016
- CochainComplex.HomComplex.Cochainproof · cited by 341
- CochainComplex.HomComplex.cocycleproof · cited by 105
Cited by168
Results whose statement or proof uses this declaration.
- CochainComplex.mappingCone.fststatement · cited by 51
- CochainComplex.HomComplex.CohomologyClassproof · cited by 49
- CochainComplex.HomComplex.CohomologyClass.mkstatement and proof · cited by 34
- CochainComplex.HomComplex.Cocycle.equivHomShiftstatement · cited by 23
- CochainComplex.HomComplex.Cocycle.ofHomstatement · cited by 23
- CochainComplex.HomComplex.Cocycle.extstatement and proof · cited by 19
- CochainComplex.HomComplex.Cocycle.fromSingleMkstatement · cited by 19
- CochainComplex.HomComplex.Cocycle.toSingleMkstatement · cited by 19
- CochainComplex.HomComplex.Cocycle.homOf_fstatement and proof · cited by 13
- CochainComplex.mappingCone.liftstatement and proof · cited by 12
- CochainComplex.mappingCocone.inrstatement · cited by 11
- CochainComplex.HomComplex.CohomologyClass.toSmallShiftedHomproof · cited by 10