Objection 1. It seems that dulia has various species. For by dulia we show honor to our neighbor. Now different neighbors are honored under different aspects, for instance king, father and master, as the Philosopher states (Ethic. ix, 2). Since this difference of aspect in the object differentiates the species of virtue, it seems that dulia is divided into specifically different virtues.
Objection 2. Further, the mean differs specifically from the extremes, as pale differs from white and black. Now hyperdulia is apparently a mean between latria and dulia: for it is shown towards creatures having a special affinity to God, for instance to the Blessed Virgin as being the mother of God. Therefore it seems that there are different species of dulia, one being simply dulia, the other hyperdulia.
Objection 3. Further, just as in the rational creature we find the image of God, for which reason it is honored, so too in the irrational creature we find the trace of God. Now the aspect of likeness denoted by an image differs from the aspect conveyed by a trace. Therefore we must distinguish a corresponding difference of dulia: and all the more since honor is shown to certain irrational creatures, as, for instance, to the wood of the Holy Cross.
On the contrary, Dulia is condivided with latria. But latria is not divided into different species. Neither therefore is dulia.
I answer that, Dulia may be taken in two ways. On one way it may be taken in a wide sense as denoting reverence paid to anyone on account of any kind of excellence, and thus it comprises piety and observance, and any similar virtue whereby reverence is shown towards a man. Taken in this sense it will have parts differing specifically from one another. On another way it may be taken in a strict sense as denoting the reverence of a servant for his lord, for dulia signifies servitude, as stated above (Article 3). Taken in this sense it is not divided into different species, but is one of the species of observance, mentioned by Tully (De Invent. Rhet. ii), for the reason that a servant reveres his lord under one aspect, a soldier his commanding officer under another, the disciple his master under another, and so on in similar cases.
Reply to Objection 1. This argument takes dulia in a wide sense.
Reply to Objection 2. Hyperdulia is the highest species of dulia taken in a wide sense, since the greatest reverence is that which is due to a man by reason of his having an affinity to God.
Reply to Objection 3. Man owes neither subjection nor honor to an irrational creature considered in itself, indeed all such creatures are naturally subject to man. As to the Cross of Christ, the honor we pay to it is the same as that which we pay to Christ, just as the king's robe receives the same honor as the king himself, according to Damascene (De Fide Orth. iv).
Source: Summa Theologica (New Advent)