The correct answer to this open question is the following.
The Catholic Church and Roman Emperor connected to each other in that they both had an intrinsic relationship of power and control over the citizens of Rome.
Let's have in mind that it was Emperor Constantine the one that established Christianity in Rome in the first place. After being a persecutor of Christians, Constantine had a dream in which Archangel Gabriel told him that if he converted to Christianity, he would win all his battles. Then, the relationship between the Roman Emperor and the Pope was a relationship based on convenience, power, and control. They needed each other to exploit the people and exert their power.