Theorems · Definition · group theory

Rep.indCoindNatIso

(k : Type u) →
  {G : Type v} →
    [inst : CommRing k] →
      [inst_1 : Group G] →
        (S : Subgroup G) →
          [DecidableRel ⇑(QuotientGroup.rightRel S)] →
            [S.FiniteIndex] → Rep.indFunctor k S.subtype ≅ Rep.coindFunctor k S.subtype

Given a finite index subgroup S ≤ G, this is a natural isomorphism between the Ind_S^G and Coind_G^S functors Rep k S ⥤ Rep k G.

Defined in

Mathlib.RepresentationTheory.FiniteIndex

Cited by

6 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupDecidableRelSubgroup.FiniteIndex