{X : Type u} →
  {G : Type u_2} →
    [inst : Group G] →
      [inst_1 : MulAction G X] →
        {H : Type u_3} →
          [inst_2 : Group H] →
            CategoryTheory.Functor (CategoryTheory.ActionCategory G X) (CategoryTheory.SingleObj H) →
              G →* (X → H) ⋊[mulAutArrow] G