Theorems · Definition · group theory
groupCohomology.cocycles
{k G : Type u} → [inst : CommRing k] → [inst_1 : Group G] → Rep.{u, u, u} k G → ℕ → ModuleCat kThe n-cocycles Zⁿ(G, A) of a k-linear G-representation A, i.e. the kernel of the
nth differential in the complex of inhomogeneous cochains.
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Groupstatement and proof · cited by 6,238
- ModuleCatstatement · cited by 1,429
- Repstatement and proof · cited by 843
- HomologicalComplex.cyclesproof · cited by 164
- groupCohomology.inhomogeneousCochainsproof · cited by 83
Cited by72
Results whose statement or proof uses this declaration.
- groupCohomology.iCocyclesstatement · cited by 27
- groupCohomology.πstatement · cited by 25
- groupCohomology.cocyclesMapstatement · cited by 19
- groupCohomology.isoCocycles₁statement · cited by 19
- groupCohomology.isoCocycles₂statement · cited by 18
- groupCohomology.cocyclesIso₀statement · cited by 15
- groupCohomology.toCocyclesstatement · cited by 6
- groupCohomology.cocyclesIso₀_hom_comp_fstatement · cited by 6
- groupCohomology.cocyclesMkstatement · cited by 6
- groupCohomology.isoCocycles₁_hom_comp_istatement · cited by 5
- groupCohomology.isoCocycles₂_hom_comp_istatement · cited by 5
- groupCohomology.toCocycles_comp_isoCocycles₁_homstatement · cited by 2