{C : Type u₁} →
  [inst : CategoryTheory.Category.{u₂, u₁} C] →
    (F : CategoryTheory.Functor C FintypeCat) →
      [inst_1 : CategoryTheory.PreGaloisCategory C] →
        [CategoryTheory.PreGaloisCategory.FiberFunctor F] →
          (X Y : C) → (F.obj (X ⨯ Y)).carrier ≃ (F.obj X).carrier × (F.obj Y).carrier