Theorems · Theorem · group theory

groupHomology.H1CoresCoinfOfTrivial_exact

∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] (A : Rep.{u, u, u} k G) (S : Subgroup G) [inst_2 : S.Normal]
  [inst_3 : Representation.IsTrivial (MonoidHom.comp A.ρ S.subtype)], (groupHomology.H1CoresCoinfOfTrivial A S).Exact

Given a G-representation A on which a normal subgroup S ≤ G acts trivially, the short complex H₁(S, A) ⟶ H₁(G, A) ⟶ H₁(G ⧸ S, A) is exact.

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality

Cited by

1 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupSubgroup.NormalRepresentation.IsTrivial