Theorems · Definition · group theory

Rep.coinvariantsShortComplex

{k : Type u} →
  {G : Type v} →
    [inst : CommRing k] →
      [inst_1 : Group G] →
        Rep.{w, u, v} k G → (S : Subgroup G) → [S.Normal] → CategoryTheory.ShortComplex (Rep.{w, u, v} k G)

Given a normal subgroup S ≤ G, a G-representation A induces a short exact sequence of G-representations 0 ⟶ Ker(mk) ⟶ A ⟶ A_S ⟶ 0 where mk is the quotient map to the S-coinvariants A_S.

Defined in

Mathlib.RepresentationTheory.Coinvariants

Cited by

8 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupSubgroup.Normal