Theorems · Definition · group theory
groupCohomology.H1InfRes
{k G : Type u} →
[inst : CommRing k] →
[inst_1 : Group G] → Rep.{u, u, u} k G → (S : Subgroup G) → [S.Normal] → CategoryTheory.ShortComplex (ModuleCat k)The short complex H¹(G ⧸ S, A^S) ⟶ H¹(G, A) ⟶ H¹(S, A).
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingGroupSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Subgroupstatement and proof · cited by 3,593
- CategoryTheory.ShortComplexstatement · cited by 1,850
- ModuleCatstatement · cited by 1,429
- Repstatement and proof · cited by 843
- Rep.ρproof · cited by 356
- Subgroup.Normalstatement and proof · cited by 334
- Rep.resproof · cited by 213
- Subgroup.subtypeproof · cited by 185
- QuotientGroup.mk'proof · cited by 90
Cited by6
Results whose statement or proof uses this declaration.
- groupCohomology.H1InfRes_exactstatement and proof · cited by 0
- groupCohomology.H1InfRes_fstatement and proof · cited by 0
- groupCohomology.H1InfRes_gstatement and proof · cited by 0
- groupCohomology.H1InfRes_X₁statement and proof · cited by 0
- groupCohomology.H1InfRes_X₂statement and proof · cited by 0
- groupCohomology.H1InfRes_X₃statement and proof · cited by 0