Theorems · Theorem · group theory

Rep.indToCoind_coindToInd

∀ {k : Type u} {G : Type v} [inst : CommRing k] [inst_1 : Group G] {S : Subgroup G}
  [inst_2 : DecidableRel ⇑(QuotientGroup.rightRel S)] (A : Rep.{w, u, v} k ↥S) [inst_3 : S.FiniteIndex],
  A.coindToInd ∘ₗ A.indToCoind = LinearMap.id

Defined in

Mathlib.RepresentationTheory.FiniteIndex

Cited by

1 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingGroupDecidableRelSubgroup.FiniteIndex