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.
On the contrary, The Philosopher says (De Anima iii, 5) that the active intellect is as a light. But light is not the same in the various things enlightened. Therefore the same active intellect is not in various men.
I answer that, The truth about this question depends on what we have already said (4). For if the active intellect were not something belonging to the soul, but were some separate substance, there would be one active intellect for all men. And this is what they mean who hold that there is one active intellect for all. But if the active intellect is something belonging to the soul, as one of its powers, we are bound to say that there are as many active intellects as there are souls, which are multiplied according to the number of men, as we have said above (Question 76, Article 2). For it is impossible that one same power belong to various substances.
Reply to Objection 1. The Philosopher proves that the active intellect is separate, by the fact that the passive intellect is separate: because, as he says (De Anima iii, 5), "the agent is more noble than the patient." Now the passive intellect is said to be separate, because it is not the act of any corporeal organ. And in the same sense the active intellect is also called "separate"; but not as a separate substance.
Reply to Objection 2. The active intellect is the cause of the universal, by abstracting it from matter. But for this purpose it need not be the same intellect in all intelligent beings; but it must be one in its relationship to all those things from which it abstracts the universal, with respect to which things the universal is one. And this befits the active intellect inasmuch as it is immaterial.
Reply to Objection 3. All things which are of one species enjoy in common the action which accompanies the nature of the species, and consequently the power which is the principle of such action; but not so as that power be identical in all. Now to know the first intelligible principles is the action belonging to the human species. Wherefore all men enjoy in common the power which is the principle of this action: and this power is the active intellect. But there is no need for it to be identical in all. Yet it must be derived by all from one principle. And thus the possession by all men in common of the first principles proves the unity of the separate intellect, which Plato compares to the sun; but not the unity of the active intellect, which Aristotle compares to light.
Source: Summa Theologica (New Advent)