Theorems · Definition · group theory
groupCohomology.cocyclesMap
{k G H : Type u} →
[inst : CommRing k] →
[inst_1 : Group G] →
[inst_2 : Group H] →
{A : Rep.{u, u, u} k H} →
{B : Rep.{u, u, u} k G} →
(f : G →* H) → (Rep.res f A ⟶ B) → (n : ℕ) → groupCohomology.cocycles A n ⟶ groupCohomology.cocycles B nGiven a group homomorphism f : G →* H and a representation morphism φ : Res(f)(A) ⟶ B,
this is the induced map Zⁿ(H, A) ⟶ Zⁿ(G, B) sending x : Hⁿ → A to
(g : Gⁿ) ↦ φ (x (f ∘ g)).
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CommRingstatement and proof · cited by 17,173
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- ModuleCatstatement · cited by 1,429
- Repstatement and proof · cited by 843
- Rep.resstatement and proof · cited by 213
- groupCohomology.cocyclesstatement · cited by 63
- HomologicalComplex.cyclesMapproof · cited by 59
- groupCohomology.cochainsMapproof · cited by 41
Cited by19
Results whose statement or proof uses this declaration.
- groupCohomology.H1π_comp_mapproof · cited by 3
- groupCohomology.H2π_comp_mapproof · cited by 2
- groupCohomology.π_mapstatement · cited by 2
- groupCohomology.cocyclesMap_cocyclesIso₀_hom_fstatement and proof · cited by 2
- groupCohomology.cocyclesMap_comp_isoCocycles₁_homstatement and proof · cited by 2
- groupCohomology.cocyclesMap_comp_isoCocycles₂_homstatement and proof · cited by 2
- groupCohomology.cocyclesMap_compstatement · cited by 1
- groupCohomology.cocyclesMap_id_compstatement · cited by 1
- groupCohomology.π_map_applystatement and proof · cited by 0
- groupCohomology.π_map_assocstatement and proof · cited by 0
- groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_applystatement and proof · cited by 0
- groupCohomology.cocyclesMap_cocyclesIso₀_hom_f_assocstatement and proof · cited by 0