∀ {k G : Type u} [inst : CommRing k] [inst_1 : Group G] {S : Subgroup G}
  [inst_2 : DecidableRel ⇑(QuotientGroup.rightRel S)] [inst_3 : S.FiniteIndex] (B : Rep k G),
  (Rep.resIndAdjunction k S).unit.app B =
    CategoryTheory.CategoryStruct.comp ((Rep.resCoindAdjunction k S.subtype).unit.app B)
      (Rep.indCoindIso ((Action.res (ModuleCat k) S.subtype).obj B)).inv