Whether the active intellect is one in all?

Objections

Objection 1 : It would seem that there is one active intellect in all. For what is separate from the body is not multiplied according to the number of bodies. But the active intellect is "separate," as the Philosopher says (De Anima iii, 5). Therefore it is not multiplied in the many human bodies, but is one for all men.
Objection 2 : Further, the active intellect is the cause of the universal, which is one in many. But that which is the cause of unity is still more itself one. Therefore the active intellect is the same in all.
Objection 3 : Further, all men agree in the first intellectual concepts. But to these they assent by the active intellect. Therefore all agree in one active intellect.