Theorems · Definition · group theory

groupHomology.H1CoresCoinfOfTrivial

{k G : Type u} →
  [inst : CommRing k] →
    [inst_1 : Group G] →
      (A : Rep.{u, u, u} k G) →
        (S : Subgroup G) →
          [S.Normal] →
            [Representation.IsTrivial (MonoidHom.comp A.ρ S.subtype)] → CategoryTheory.ShortComplex (ModuleCat k)

Given a G-representation A on which a normal subgroup S ≤ G acts trivially, this is the short complex H₁(S, A) ⟶ H₁(G, A) ⟶ H₁(G ⧸ S, A). (This is a simplified expression for the degree 1 corestriction-coinflation sequence when A is S-trivial.)

Defined in

Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality

Cited by

7 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupSubgroup.NormalRepresentation.IsTrivial