Here’s the section we read from Aquinas:
I answer that, Wherever there are several authorities directed to one purpose, there must needs be one universal authority over the particular authorities, because in all virtues and acts the order is according to the order of their ends (Ethic. i, 1,2). Now the common good is more Godlike than the particular good. Wherefore above the governing power which aims at a particular good there must be a universal governing power in respect of the common good, otherwise there would be no cohesion towards the one object.
Hence since the whole Church is one body, it behooves, if this oneness is to be preserved, that there be a governing power in respect of the whole Church, above the episcopal power whereby each particular Church is governed, and this is the power of the Pope.
Consequently those who deny this power are called schismatics as causing a division in the unity of the Church. Again, between a simple bishop and the Pope there are other degrees of rank corresponding to the degrees of union, in respect of which one congregation or community includes another; thus the community of a province includes the community of a city, and the community of a kingdom includes the community of one province, and the community of the whole world includes the community of one kingdom.
ST Supp. Q. 40, A. 6.